Aunt May in the comics
Aunt May and her husband, Ben, took their nephew, Peter, in after the death of his parents and raised him well. After Ben's death, life became a struggle with money problems and Peter did his best to help.
The problem is that Peter's secret life as Spider-Man endlessly complicates both his and his aunt's lives. Aunt May lives in constant worry for her "frail" (but now unaccountably secretive) nephew who insists on a job as a freelance photographer. Parker is determined to capture Spider-Man in action, frequently submitting pictures of him to the Daily Bugle; Spider-Man is a vigilante whom Aunt May fears because of her unquestioning acceptance of the Daily Bugle's smearing.
Meanwhile, Peter fears for his Aunt's well-being and the fatal shock that could result if she ever learns about his career as Spider-Man. This problem served as an easy crutch for dramatic tension in the comics for years, with Peter being torn between dealing with major crises while his Aunt needs nearly constant care. This conflict took on a bizarre turn when Aunt May had his enemy, Doctor Otto Octavious (a.k.a. Doctor Octopus) as an apparent sweetheart: Peter struggled to deal with his enemy's game while not hurting his Aunt.
For decades, Aunt May was depicted as a stereotypical near senile old crone, especially after co-creator Steve Ditko left the book and the subtle undertone of her inner strength was lost. Later writers, like J. Michael Straczynski, of Babylon 5 fame, have managed to recapture that quality and restore the nuances in her character. For instance, JMS had May finally learn about her nephew's secret life once and for all. That resulted in a heartfelt discussion in which Aunt and Nephew confess their darkest secrets and each learned that the other was far stronger than they imagined.
In the Ultimate version of Spider-Man, Aunt May is a slightly younger woman who is a pillar of strength who takes no guff even as she deals with her nephew's suspicious and secretive behaviour.
Aunt May in the film
In the 2002 Spider-Man movie, Aunt May and Uncle Ben take care of Spider-Man, and that Uncle Ben is killed by a carjacker who in turn is killed by Spider-Man. However, Aunt May is injured by the Green Goblin after he learns of Spider-Man's identity and starts to lash out at his beloved. Green Goblin then makes a failed attempt to kill Mary Jane Watson, Spider-Man's girlfriend, before the Green Goblin is killed.