If you are not familiar with the series but think you might enjoy a whimsical off-the-wall sci-fi comedy, there’s no harm in starting with this one.
Agent J (Will Smith) and his laconic weather-beaten partner Agent K (Tommy Lee Jones) work for a super-secret organization called MIB. Their job is to suppress evidence of UFOs and make sure that aliens visiting Earth behave themselves.
Boris The Animal (Jemaine Clement) is a very bad alien whom Agent K arrested long ago. He is being held in a super-super-maximum security prison on the Moon, but at the start of the movie he breaks out and goes after Agent K. More specifically he gets a time-travel device, goes back to 1969 and kills Agent K before he can arrest him.
This leads Agent J to travel back to 1969 (a time when alien influence on our culture was at its height) in order to thwart him. There he meets the young Agent K (Josh Brolin) who seems much more voluble. And that’s pretty much it: a setup for elaborate comedic riffs on aliens, time travel and pop culture. And there’s an excellent ending which I found highly satisfying.