Zambia has three distinct seasons, and when you visit depends entirely on what you want to do.
Cool dry season (May to August). This is the most comfortable time to visit. Temperatures are pleasant during the day and cool at night -- bring a fleece for early morning game drives. The bush starts to thin out and wildlife becomes easier to spot as animals congregate around permanent water sources. Victoria Falls is still flowing strongly from the tail end of the rains. This is peak season for South Luangwa and Lower Zambezi, and lodges fill up fast.
Hot dry season (September to October). The best months for serious wildlife viewing. Vegetation is at its thinnest, waterholes are shrinking, and animals crowd together in spectacular concentrations. Temperatures climb into the high 30s, and it can feel relentless by mid-afternoon. South Luangwa is extraordinary at this time -- expect large herds of elephant, prides of lion on the hunt, and leopards in every other tree. Victoria Falls is at its lowest flow, but this is when you can swim in Devil's Pool right at the lip of the falls.
Wet season / emerald season (November to April). The rains transform Zambia into a lush green landscape. This is when Victoria Falls is at its most powerful -- by March and April, the spray can be seen from 30 kilometers away and you will be drenched just standing at the viewpoints. Many safari camps close because roads flood and become impassable, but a few lodges in South Luangwa stay open and offer excellent birdwatching and green-season rates at a fraction of peak prices. The Bangweulu Wetlands are best visited in the wet season for the shoebill stork. Fly-in safaris make remote areas accessible even when the roads are not.
For most visitors, June to October is the sweet spot -- dry weather, good wildlife, and all the lodges open. But if you are flexible on dates and willing to get a little muddy, the emerald season offers Zambia at its most dramatic and its most affordable.