Fires on the savannas are not always caused by natural means. In some cases they are set intentionally. The Maasai tribe, for example, would create a controlled burn of their grazing lands every years in order to stop drying, nutrient poor grasses from using water. This gives the soil a better chance of producing thick grass for the growing season.
The wet / dry seasons in east Africa are due to the monsoon. Each year, moisture collects in the air above in the southern Indian Ocean. It then moves north, eventually reaching the Himalayas, releasing moisture as it passes. Then, after losing most of its moisture, it heads south and releases more moisture, but of a shorter duration. Every year it repeats this cycle. The impact on east Africa is that for around seven weeks during March and April, it rains every day. This is known as the long rains. There is then a drying out period of about six months as the monsoon continues on to the north. It returns to east Africa in November, at which time it rains every day for about a month, followed by a shorter drying period. This is known as the short rains. A characteristic of the rains in east Africa is that it rains every evening and through the night, finishing up by mid-morning, providing a daily break of about twelve hours.