Each of the somotypes is named after a part of the embryo during development: the ectoderm (literally "outer skin") becomes the skin and nervous system, the mesoderm ("middle skin") becomes muscles and bones, and the endoderm ("inner skin") becomes the internal organs. Thus, ectomorphs are skinny, mesomorphs are muscular, and endomorphs are fat. The somotype theory was supposed to predict people's behavior based on their body type, but of course this oversimplifies psychology (one's personality is only partially shaped by one's body type), confuses causation and correlation (are skinny people bookish because of their "somotype" or are they skinny because they're bookish?), and plays to stereotypes (such as the old one of all fat people being easy-going…one that even Shakespeare played into).
One of the most difficult barriers to gaining muscle for ectomorphs is that most of us have very high metabolisms--that is, we use up a lot of calories every day. Since one needs a surplus of calories to gain any weight (either fat or muscle), ectomorphs have to concentrate on what, when, and how much they eat even more than non-ectomorphs; otherwise, they burn up all the calories and nothing is left to build muscle. The silver lining to this cloud is that ectomorphs generally don't need to worry too much about gaining too much fat.
Especially people like me who enjoy long-distance/endurance sports (such as cross-country running, triathlons, etc.) will tend to have more "slow-twitch" (Type I) than "fast-twitch" (Type II) muscle fibers. Ectomorphs also tend to have less muscle fibers in general...since weight training tends to increase the size of fast-twitch muscle fibers, this means that it's harder for ectomorphs to respond to weight training. It's unclear whether one can change the proportion of fast- and slow-twitch fibers or the number of those fibers. Stephen Seiler's Exercise Physiology page has all kinds of information about muscle fiber types and other science behind exercise, if you want to learn more.
Many ectomorphs have long limbs and short muscles, which one gives one less leverage when trying to lift weight. One test of this is to flex your biceps and see how many fingers you can fit between the muscle and your forearm. If you can fit three (or four, in my case!) fingers in the gap, you have relatively short muscles and long tendons--making it more difficult to lift weight and thus gain weight, due to the mechanical disadvantage.
Ectomorphs tend to have thinner, less dense bones, which makes it more difficult to support high weights. One test of this is encircling your wrist with the other hand's thumb and middle finger. If your fingers touch (or even overlap, as mine do!), then you have pretty thin bones. Some argue it is possible to increase bone density over several years of training, but you're pretty much stuck with your bone size.