Why does the rainy season in the tropical dry Forrest and tropical savanna come

The simplest explanation I can think of is the warmer it is, the more water will evaporate. In warmer months, more water evaporates, and then more clouds build up, which causes more rain.

I believe these rains are called monsoon.

The global atmospheric circulation model shows how air near the equator tends to rise, due to the temperatures being higher than the surrounding tropics. This leads to high instability and low pressure, acting like a conveyor belt for water and creating high levels of precipitation.

Because of the Earth's axial tilt, the area over which this low pressure zone sits changes from season to season. At its most extreme, the solar equator (the area where the sun is directly overhead) reaches as far as the Tropics of Cancer and Capricorn, and the band of rain oscillates with it.

This results in the perception of seasonal rain. In fact, this rain exists all year round, but the band moves north and south with the seasons, bringing heavy rain in the summer and leaving drought in the winter, creating a monsoon affect in many African countries.