The Tsodilo Hills are formed from what's technically known as 'micaceous quartzite schists'. These metamorphic rocks started out as shales, probably deposited as mud on the surface of an ancient sea. Great heat and pressure in the earth changed them, and you can see the small crystals of minerals formed during this process if you look carefully.
Tsodilo's schists have particularly high mica and quartz contents, and a coarse-grained surface. Conveniently, this texture means that rocks give a good grip to rubber-soled shoes, so they're relatively easy to clamber around. In many places there are piles of boulders, and you'll often need to hop between these if you want to explore the hills.
There are a few permanent springs of water in the hills, but these are very difficult to find without a local guide. They were certainly important to the early inhabitants of the area though, as they would have been the only water sources for miles around.