It pretty much looks like someone punched me so hard that they left a dent right in the middle of my chest. Mother dearest calls it my "cave," and little brother says my heart is a black hole that sucked my sternum in. I have moderate congenital pectus excavatum, a common but surprisingly not well-known skeletal defect.

How it Happens
PE is caused by a deformity in the costal cartilage (i.e. the cartilage connecting the sternum to the ribs). Instead of growing straight out and across the chest, it grows downwards, towards the spine, pulling the sternum along with it. Because of this, the deformity tends to become much more pronounced during puberty. The ribs are also slightly affected, and many people with PE also have flared ribs. A potbelly is a common result as well, due to the posture associated with PE. People with the deformity tend to slouch to an extreme degree, although it is unknown if the pectus causes the slouching or vice versa. They do, however, seem to feed off each other: worse posture can worsen the pectus, and a more severe defect is detrimental to posture. It is suspected that this is because of the weakening effect that both cause to the intercostal muscles, which are the muscles between ribs that are partially responsible for posture and also for deep breathing.
My PE is congenital, meaning I was born with it, and it has yet to be determined if it is a symptom of another disorder. PE is associated with syndromes that affect the body's cartilage, and I won't list them here because mtw has provided quite a few in the write-up above.*

Effects on the Body
As mentioned above, PE tends to go hand-in-hand with bad posture. It can also compress the chest cavity in more severe cases. Rarely, the compression is so severe as to require emergency operation. In most cases the effect is minimal and requires no medical attention. The depressed sternum can, however, negatively affect lung capacity and heart functioning. The way these effects are measured is covered in the section entitled "Doctors and Tests." Lung capacity is affected not only by the depression of the sternum itself, but also by the weakening of the intercostal muscles, which makes breathing less efficient.
Cosmetically, PE is associated with flared ribs and can sometimes cause uneven growth of the ribcage. In my case, for example, the right half of my ribcage is very even and round, and the left is more angular. This asymmetry can affect the growth and evenness of breasts as well, and cause nipples to be "cock-eyed" (i.e. facing inwards instead of forward), although PE is most common in males.

To measure the depth of your PE, you should lie flat on your back. Place a straight-edge flat across your chest, left to right, next to the deepest part of your sternum. This serves to indicate the level your chest wall would be at with a normal sternum. Place the end of a ruler at the deepest part, and check the number at the level of the straight-edge. If you choose to consult a doctor about your pectus, he or she will likely do this to determine the severity. Don't be alarmed if you have severe pectus (don't quote me on this, but I believe about 2 inches constitutes "severe," 1-2 constitutes "moderate," and less than 1 is "mild." Mine was over 2.5 before surgery and is about 1 inch three years after, although immediately after it was perfectly and beautifully flat). The physical effect of pectus varies greatly, and the severity by actual number pretty much only affects what your health insurance company has to say. Mild pectus can have debilitating affects on the heart and lungs, and severe pectus can have no effect at all. It varies greatly from person to person. The best thing you can do is probably just go get it checked out.

Doctors and Tests
When I was born, my pectus was evident. My mother tells me it looked like a thumbprint on my chest. I never really noticed it at all during childhood, but, as is typical for people with PE, it got much deeper during puberty and one day I just kind of realized my chest was dented. We spent a lot of time doing research on the internet, mostly for my mom to console me, because any 14-year-old girl who finds out her chest is literally caved in is going to be at least a little upset. We went to my general physician first, who, not uncommonly, had no idea where to send me. So she recommended an orthopedic doctor, who then sent us to a cardiologist. Surprisingly, cardiologists are actually the ones who deal with pectus and operations on it, because even though it is a bone/cartilage defect, it primarily affects the heart and lungs.
The consultation with the cardiologist told us that my pectus was severe, and she ordered up an MRI, respiratory function tests, and meetings with both a plastic surgeon and a physical therapist. The MRI determined how the pectus affected my heart (only slight compression, nothing alarming), and the respiratory tests, how it affected my lungs (my lung capacity was determined to be at 78% of my body's potential "average," with the cut-off point for surgical intervention at 80% - aka, just enough to warrant correction, but just goes to show that the depth of your PE is not necessarily correlated with actual severity). The physical therapist worked with me on developing stronger intercostal muscles, as people with PE tend to have very weak intercostals (like slouching, it is not known if weak intercostals and other breath/posture muscles can cause pectus, but they contribute to it and vice versa), and ribcage/shoulder mobility, which is often limited by PE. The plastic surgeon discussed post-surgery options with me, which will be covered in the next section.
After all of these many appointments, we headed back to the cardiologist and it was decided that I would be a good candidate for surgery both physiologically and cosmetically.

Repairing PE
Physical therapy is a major part of PE repair. Research is being conducted on non-surgical ways to improve PE, but for now, operations are the only definitively effective method. Without physical therapy, however, they are far less likely to be successful. As mentioned briefly above, strong intercostal muscles and good posture are necessary to prevent PE from coming back after surgery. Physical therapy helps develop these muscles both before and after the operation so as to prevent the necessity of a second surgery years later. When I stopped doing physical therapy only about two months after my surgery (I was cocky and naive - I was all better! No need for therapy, right?), my pectus worsened significantly within the next half a year or so and while it is not as deep as it once was, I lost the nice flat sternum I had when I woke up after the operation. I don't know if I'll ever repeat the surgery, but if I do, physical therapy will play a much greater role than it did the first time around.
There are several options for surgery: the Ravitch procedure, the Nuss procedure, and the Leonard procedure.
The Leonard procedure has been developed in the time after I had my operation so I know very little about it. It involves using wires to reshape the sternum, and requires the patient to wear a brace for several months after the initial operation.
The Nuss procedure is also fairly new, and while it is considered minimally invasive, it's pretty risky. In the Nuss procedure, a custom-made metal bar is inserted into the chest from below the armpit. The bar is slightly curved, and once it has been inserted, it is rotated, "popping" the chest into the correct position. It requires a follow-up surgery later (at the doctor's discretion - usually 6 months to a year or more) to remove the bar. Other than typical surgery risks such as anesthesia risks and infection, the Nuss procedure also carries the risk of puncturing the pericardium (the protective casing around the heart), which could in turn infect it, which is dangerous to cardiac health. It has a shorter recovery period than the Ravitch, which is the procedure I had done and is of course the one I am most familiar with.
Essentially, the Ravitch procedure, which is the oldest one (and far more invasive and time-consuming as far as time spent under anesthetic), involves removing the intercostal cartilage itself (see How it Happens). The casing that the cartilage grows in is left intact, so that as it grows back, it has a pathway back to the sternum, and so that it can grow back faster (the casing produces cartilage cells). After the cartilage has been removed, the sternum is scored to break at certain points (determined by the surgeon, dependent on the patient's specific shape) and then "lifted" into place. A bar** is then placed under the ribcage to hold the sternum up. A follow-up surgery is also required to remove the bar. This procedure leaves a much bigger scar - mine is horizontal across my chest, just below the breasts and about 6 inches long.
A plastic surgeon is usually consulted about the appearance of the sternum after the surgery. First of all, if the very top of the sternum is affected by PE (between the top 2 ribs), this portion of the chest will not be cosmetically improved by surgery. Second, the sternum is very bumpy and uneven after surgery (because it has been broken), and since people with pectus tend to be thin, these bumps are often visible through the skin. Plastic surgeons can insert synthetic materials to fill in grooves and smooth out the appearance of the chest. This can usually be done at the same time the bar is removed.

*I've cited mtw's w/u above because it's good and I don't expect it to disappear, but if it does, please message me and I will add the information that I omitted.
**I should note that even though I had the Ravitch procedure, I did not have a bar put into place. Because I am so thin, the bar was actually visible through my skin, and would have caused me to heal with a ridge in my chest where it was placed. The surgeon left the bar out and I wore a brace for a year instead, counting on physical therapy and good posture to keep my sternum in place. It was somewhat effective: my pectus did come back, but it is much less severe and the surgery had a huge effect on my breathing, which is vital for me as a singer. I feel that my loss of commitment to physical therapy is more responsible for the PE's return than the lack of a bar, although of course I can't say for sure.