Botswana has a hot, wet summer (between October and April), and a cooler, dry winter (from May to the end of September). Winter is traditionally high season in terms of price and visitor numbers, while summer is the quieter off-peak (or “green") season. It's not quite as simple as this, but as a guideline, visit the Okavango between May and November and the Kalahari between January and March if your primary objective is to see wildlife. If your interests are broader, it's best to have a chat so we can recommend the best time for you.
In a bit more detail:
During the summer, the rains fall, the grass grows lush and high and water is plentiful which means that the game is dispersed and tricky to spot amongst the vegetation. However, this time of year is scenically very beautiful as everything bursts into life. Between November and March, the Delta comes alive with migratory birds and so this is one of the best times to visit if you are an avid twitcher. For the botanists or those that simple love trees and flowers, December to May is when most plants flower and the bush is lush and green. You will need to prepare yourself for the prospect of a proper African downpour, though, and some areas will be off-limits as the roads can be pretty sticky. Temperatures can rise to 40°C during the day and remain at 25°C at night.
The winter months are much dryer with game concentrating at the depleting water sources. Un-obscured by tall grass, herbivores and carnivores are much easier to spot and it is also less likely that you will spend some time helping to dig the safari vehicle out of the mud. The pleasant temperatures mean that you can spend more time comfortably out and about too. Temperatures will normally be in the 20’s during the day and nights can be quite chilly.
As with any destination, the best times of year command peak prices. It is possible to save a bit if you are prepared to travel outside of these times and maybe risk the odd shower or the chance that you may not see wildlife-on-a-plate. The up-side is that you will probably have the place to yourself.