It’s actually a year-around phenomenon. The simple story is that these vast herds are on a continual search for food and water and spend the entire year moving in a more-or-less clockwise direction around the Serengeti eco-system.
Weather, specifically rain, is the driving force of migration, so any change in the seasonal weather patterns (more, less or no rain) has a huge impact on the location of the migration and the size of the herds.