During the dry season at the Serengeti Plains the conditions are very harsh, particularly for animals for which their existence, to a great extend, depends on water (drinking and water needed to grow grass in the plains that represents their only source of food).
This is the reason behind the "great migration", in which many thousands of gnus and zebras migrate north toward the Masai Mara, in Kenya, mostly following the rains. In the Masai Mara the animals will find abundant fresh-green pastures and water.
The animals that lag behind during the migration and stay in the Serengeti would depend mostly on a few, scarse water holes which are in great demand to all other resident animals including predators like the big cats. Many times Lions will stay nearby these waterholes knowing that animals will be "forced" to come and drink, usually becoming easy prey.