There were many different provisions in the Real ID Act of 2005, but the most important (and the one I assume you are asking about) is the requirement that all states start requiring birth certificates or passports or other such kinds of proof that a person is in the country legally before issuing them a driver's license. If a state does not require such things, its drivers licenses will not be accepted for such things as boarding airplanes or entering federal buildings.
The major reason that the government wants to do this is terrorism. The 9/11 attackers were able to get drivers' licenses quite easily even though they were not in the US legally. The government wants to ensure that people have to prove who they are and that they are here legally before they are able to get a form of ID that tends to be accepted everywhere.
The major argument against this is that it makes things very difficult for people who may lack, through no fault of their own, the sorts of proof that the law requires. This is especially true for older people whose birth certificates may have long ago disappeared. If such people are unable to get ID, they will have trouble with all sorts of things like getting Social Security. You can find a link to a site that opposes this law below.