Many of Disney's classic cartoons are based on Grimms' fairy tales and other traditional stories. Such stories often featured characters whose mothers died in childbirth or otherwise perished. That leaves the door open for the ubiquitous "wicked stepmother" who invariably places the heroes in great peril. In adapting these stories to the big screen, Disney took certain liberties with the story. The classic tropes remain in many of them, however... including departed mothers and wicked stepmothers.
According to Just Disney, Walt Disney's own mother died amid tragic circumstances. Following the success of "Snow White," Walt and his brother bought their mother Flora a new home in Burbank, California. The home's gas furnace had significant problems, however, and despite Disney's efforts to fix it, it caused a tragic accident. Flora died of asphyxiation in her home in late 1938. Though it's speculative, Walt's trauma at her loss may have seeped into his subsequent movies, creating a recurring theme.
The death of the main character's mother entails ready drama that enhances the overall story: giving the hero a trauma to overcome and eventually make peace with. The most prominent example is Bambi, whose mother dies at the hand of a human hunter. Not only does it give Bambi a tragedy to come to grips with, but it also makes a potent point about the evils of the human world. A less dramatic example occurs in the movie "Lilo and Stitch." Lilo and her sister have lost their parents and struggle to make ends meet, providing a fulcrum for Lilo's loneliness, which is alleviated with the arrival of Stich.
Mothers represent a comforting theme in movies and literature: they love you and keep you safe. The heroes in many movies -- especially those who participate in epic journeys like Disney's heroes do -- must learn to grow and stand on their own. They confront the dangers of the outside world without their parents to rely on them , and thus learn to stand on their own. The death or absence of a mother helps drive that point home, removing a source of comfort and forcing them to confront the challenges of the story alone. This occurs even in Disney movies where the mother lives, such as "Dumbo" and "The Princess and the Frog." In such movies, the mother is left off screen or otherwise out of commission so that the hero can face his or her obstacles alone (though there's sometimes a cathartic reunion at the end -- as in the case of "Dumbo" or "Tangled" -- to give the film a proper sense of closure).