Semantic memory consists of your general knowledge about the world. For example, you know what a poodle is, you know that it's a kind of dog, that beagles and rottweilers are other kinds of dogs, and that dogs can be trained, but nonetheless tend to poop in inconvenient places.
Now, you probably don't remember where you learned all of that, but you know it anyway. According to Endel Tulving, who first came up with the distinction, that's a defining feature of semantic memory--it's something you know, even though you can't remember where or when you learned it. (If you have a memory about a particular pooping dog, or your best friend's rottweiler, or anything else that involves a specific event, then that's an episodic memory.)
The neurobiology of semantic memory remains unclear, but some recent evidence suggests that the lateral temporal lobes play an important role. In a rare disorder called semantic dementia, this brain region degenerates, and patients slowly lose their knowledge about the world. One patient, for example, no longer knew anything about teapots; another couldn't figure out what to do with a clothespin.
Semantic-dementia patients are sometimes mistaken for visual agnosics, but there's an important distinction between the two. Patients with visual agnosia cannot recognize a teapot by sight, but they can usually answer properly if you ask them how one uses a "teapot," and they may be able to make tea without difficulty. A semantic dementia patient, on the other hand, can neither recognize the teapot nor explain its function.
Also, aphasic or anomic patients don't necessarily have problems with semantic memory. Aphasics often lose the ability to think of specific words, but they often know what they're trying to say (just as you do when you say "Give me the...uh...uh...the THING, damnit! You know what I mean!"). In the example above, an aphasic might not be able to remember the word "teapot," but would still know what it was and how to use it; he would know everything about it except its name.