Just south of the equator, Tanzania is huge and its sheer size means that the climate varies considerably within it. However, generally the main rainy season, or the 'long rains', lasts during about March, April and May. Afternoon tropical downpours are the norm – which are heavier and more predictable beside the coast and on the islands. The humidity is high and daily temperatures reach the low-mid 30°s.
The long dry season lasts throughout June, July, August, September and October is when rainfall is unusual, even on the islands. Temperatures vary hugely with altitude and location, but it's usually a fine, clear sky and sunny weather – it's a great time to visit Tanzania. During November and December there's another rainy season: the 'short rains'. These are much lighter than the main rains and less reliable.
If it has rained during the short rains, then it normally dries up for a few months, January and February, which is Tanzania's 'short dry season', before starting to rain again in earnest in March.