A microcosm is a representation of something on a very small scale. Notice the beginning, "micro." What other words use that prefix? There is "microscope," "microsurgery," "microeconomics," and so on. All of these involve something very small, don't they?
Now, think about all the different kinds of people you know. There are different types of people, aren't there? Some are good at doing things with their hands, some are good with books, and some are natural athletes. Some of the people you know are shy, while others are aggressive. Some are nice, while some are cruel. The characters in the book represent different kinds of people, don't you think?
Now, think about the world in general. Good things happen, and bad things happen. Sometimes man must battle nature. Sometimes man must battle other men, and sometimes man must battle himself. All of these are elements of the world we live in.
A microcosm is a small group of people who are as varied as people in the real world, who must deal with the same kinds of battles that people deal with in the real world, but the world is limited because there are so few boys, and all of them are on the "limited" world of an island.