Drivers licenses and other IDs are issued by the individual states, which can be issued by the states to anyone they decide to according to state laws. But the federal government (mostly just the TSA which is a part of the DHS) wanted to set a minimum standard for issuing IDs and so if you go through the process of proving you are who you say you are you get a state issued ID with a special star on it that indicates that the US government has 100% verified your identity.
Oh, and the DHS has just said that a real id is too unreliable to confirm your identity.