Botswana has two main seasons, and when you visit depends on what you want to see.
Dry season (May to October) is peak safari season. Skies are clear, vegetation thins out, and animals concentrate around water sources -- making them easier to spot. The Okavango Delta is at its fullest from June to August, when floodwaters from Angola's rains finally arrive. This is the best time for mokoro trips and delta wildlife. Nights can be genuinely cold (near freezing in June and July), so bring warm layers for early morning game drives.
Green season (November to April) brings rain, lush landscapes, and dramatically lower prices. The Makgadikgadi Pans fill with water, drawing flamingos and the great zebra migration (December to March). Birdwatching is superb -- migratory species arrive from Europe and central Africa. The Kalahari bursts into green. The downside is that some roads become impassable, some camps close, and mosquitoes are at their worst. Afternoon thunderstorms are frequent but usually short.
Shoulder months (April and November) can offer a good balance -- fewer crowds, decent weather, and transitional wildlife patterns.
If your priority is the delta and big game, visit between June and September. If you want the pans, the migration, and better rates, aim for January to March. Avoid the very hottest weeks in October if you can -- temperatures regularly exceed 40C and the landscape is parched.