Bates distribution is a type of probability distribution. Probability distributions tell us how likely something is to happen. In the case of the Bates distribution, it shows us how likely an event is to happen in a certain number of trials. To explain it further, let's take an example.
Imagine we are flipping a coin. We know that in each flip, there is a 50/50 chance that it will either be heads or tails. The Bates distribution would tell us how likely it is that we will get a certain number of heads and tails in a certain number of flips. For example, the Bates distribution might show us that after 10 flips, we are most likely to get five heads and five tails, but we might also get six heads, four tails, or any other combination of heads and tails.