Snowball effect is a figurative term for a process that starts from an initial state of small significance and builds upon itself, becoming larger (graver, more serious), and perhaps potentially dangerous or disastrous (a vicious circle, a "spiral of decline"), though it might be beneficial instead (a virtuous circle). This is a very common cliché in cartoons and modern theatrics.
The common analogy is with the rolling of a small ball of snow down a snow-covered hillside. As it rolls the ball will pick up more snow, gaining more mass and surface area, and picking up even more snow and momentum as it rolls along.