The thyroid cartilage is the largest of the cartilages of the larynx. It is a large angled plate which forms the front of your windpipe. The Adam's apple is the notch at the top of the thyroid, called the thyroid notch (even if you are female, you still have a notch, and can still feel it; it's just not as visible).
Thyroid is Greek for 'shield-shaped', but it's not quite the shape that most of us picture shields as being. The thyroid cartilage is made of two plates (the thyroid lamina) set at an obtuse angle. It has two sets of horns on the outer edges; the superior cornu are a set of large horns sticking up from the top corners; the inferior cornu are a set of smaller horns sticking down from the bottom corners. An easy way to picture it is to take your two hands and hold them together side by side, palms facing you. Push your hands together, until the pinkies in the center are pushed back behind your ring fingers -- you just made the thyroid notch! Now you will need to use your imagination; specifically, imagine that your thumbs are long and skinny, and stick both up and down; if you have a hard time with this, you could simply tape pencils to your thumbs. Now hold your hands up and curve them around in front of your throat. That's your thyroid.
The thyroid sits on top of the cricoid cartilage, the inferior cornu sitting on top of facets on either side of the cricoid lamina. These points of articulation are known as the cricothyroid joint. The two cartilages are joined by the cricothyroid muscle. This muscle has two heads, the pars recta and the pars oblique; both originate at the lateral surface of the cricoid cartilage. The pars recta inserts at the inferior border (i.e. 'the bottom') of the thyroid, and the pars oblique inserts at the anterior surface of the inferior cornu where it joins the main body of the thyroid. When contracted, these muscles pull the front of the thyroid cartilage downwards, pivoting over the cricothyroid joint. The vocal folds stretch from the thyroid to the arytenoid cartilages (which rest on the cricoid); thus, when the thyroid rocks forward the vocal folds are stretched tighter.
The antagonist of the cricothyroid muscle is the thyroarytenoid, which originates at the lamina of thyroid cartilage just below the thyroid notch and attaches to the arytenoid cartilages (which rest on the cricoid, remember?). When tensed, the vocal folds are shortened and thickened. These two muscles rocking the thyroid cartilage back and forth are the primary of controllers of pitch in the human voice. When the vocal folds are stretched tight and thin, pitch rises; when thick and fat, pitch falls.
The superior cornu of the thyroid articulate with the hyoid bone. Some people have a small cartilage sitting atop the superior cornu, called the tritical cartilages. Some do not. The presence or absence of the tritical cartilages do not seem to have any noticeable affect on laryngeal function (or anything else).
There are a number of other muscles that attach to the thyroid, but they are somewhat less interesting. Aside from controlling pitch and protecting the larynx, the the thyroid provides structure and support for the structures involved in phonation and swallowing; the epiglottis arises from the inner surface of the thyroid, and both the vocal folds and the false vocal folds (which close to protect the airway during a swallow) are attached to thyroid.