They want a better life for themselves and their families.
Throughout history, this has been the reason for immigrants coming to America. The quote imprinted on a plaque at the Statue of Liberty says it well: "Give me your tired, your poor, your huddled masses yearning to breathe free." America is seen as the land of opportunity to build a life better than where they had been before.
(The quote on the Statue of Liberty plaque, by the way, comes from the poem, "The New Colossus," which was written by American poet Emma Lazarus in 1883 as part of an effort to raise money for the construction of a pedestal for the Statue of Liberty.)