Generalist animals are those adapted to a wide range of environmental circumstances and food sources, while specialist animals are really good at one narrow thing they do. An example of a generalist would be mice, which can adapt to practically any environment and consume a variety of seeds, grains, and nuts. An example of a specialist would be the koala, which lives in eucalyptus trees and exclusively consumes eucalyptus leaves, one of the only animals capable of doing so.
In general, generalist animals appear to be more successful than specialists, as they can take advantage of a wider range of circumstances. The downsides of generalism are stress and competition — because they compete in crowded biological niches, generalists have to elbow other generalists out of the way to survive on a fixed amount of nutrients. An example of this behavior is found in rats, which habitually kill mice. This behavior, known as muricide, is partially about eating the mouse for food, but only a portion of the mouse is usually consumed, signifying it may be more about eliminating competition. Being a generalist is tough work.
Meanwhile, specialists can pretty much enjoy their narrow niche without much competition. Koalas, for instance, stay high up in the trees doing little but sleeping and eating, and they are too large for anything there to predate on them. Walruses are specialist animals that live in the far north, surviving the freezing cold with a layer of blubber several inches thick. They use their snouts and specialized mouths to dig molluscs out of the sea bed and suck them out of their shells. The giraffe would be another specialist, picking succulent leaves off the tallest trees using its extremely long neck.
Examining the adaptations used by both generalists and specialists can be informative from an evolutionary perspective. Specialists have evolved to adapt to thousands of unique niches, while generalists compete in huge numbers for the easy-to-get resources of central niches. Generalists tend to evolve somewhat more quickly than specialists, being put under greater evolutionary pressures. When a specialists' niche is disturbed — say through deforestation — it can suffer terribly and even go completely extinct, however. Without flexibility in its diet or mode of living, the specialist dies. Either immediately or in a few million years, some other animal may evolve to take over that empty niche.