So far as I know, the DREAM Act has not yet become law. It has been debated in Congress, but has not yet become law. President Obama and some Congressional leaders have both proposed the basic outlines of new laws that are meant to do all or part of what the DREAM Act would do. However, nothing has been passed.
The DREAM Act is a law that would make certain illegal immigrants legal. Specifically, it is meant to apply to people who were brought illegally to the US when they were children, not those who came on their own as adults. It would apply to people who have not gotten into any legal trouble and who have been in the United States for five consecutive years (some other restrictions would apply). If such people were to apply for the act and be accepted, it would then give them six years of temporary legal residency. During those six years, they would need to complete either two years of military service or two years at a four-year college. If they were to fulfill these requirements, they would be given permanent resident status, which allows them to live in the US permanently and to apply for citizenship.
Again, however, this law has not been passed.