Jean Reno's Leon is a not-particularly-bright hitman in New York, working for the mob as represented by Danny Aiello's Tony. Although suffering from some mental disabilities - or possibly because of them - Leon happens to be particularly good at his job.
Natalie Portman's Mathilda is a twelve-year-old girl living with her family in the same apartment block as Leon, on whom she has a crush. Her father has fallen foul of another organised villain, Gary Oldman, and when tragedy strikes, Leon unwillingly takes her in. Mathilda works out what Leon does for a living very quickly, and insists that he teaches her how to 'clean', so that she can get revenge for her family.
According to IMDb, Leon is an expansion of a character that appeared in La Femme Nikita briefly, and Besson wrote the film for Reno very quickly. What he's written is very good, and also the best thing I've seen Portman in.
The relationship between the two leads is an uncomfortable watch; Mathilda is bright, sharp, precocious both sexually and in terms of understanding other people, and she manages to deliberately manipulate Leon to keep her safe; Leon's own defence against her turns out to be his own limited understanding of people and their levels of sophistry.
In addition to the two leads, Oldman is, of course, a joy to watch. Aiello, too, is interesting, and his story arc doesn't end up where I'd expected.