Mutant Registration Act is a legislative bills which, when passed into law, enforce the mandatory registration of superpowered individuals with the government made by Robert Kelly.
In the first X-Men movie the events of the movie are precipitated when Senator Robert Kelly introduces a Mutant Registration Act to the Senate.
It is the prospect of this proposed legislation that motivates Magneto in his schemes in the film, as he sees it as persecutory towards mutants. He is eventually successful in replacing Kelly with Mystique, who impersonates the Senator and removes the Act from consideration.
In the second movie, the Mutant Registration Act is briefly mentioned when Storm speculates that Nightcrawler's attack on the White House might lead the government to reintroduce the legislation.