"Normalization" is an arithmetical procedure carried out to obtain a set of probabilities summing to exactly 1, in cases where we believe that exactly one of the corresponding possibilities is true, and we already know the relative probabilities.
For example, suppose that the odds of Alexander Hamilton winning a presidential election are 3 : 2. But Alexander Hamilton must either win or not win, so the probabilities of him winning or not winning should sum to 1. If we just add 3 and 2, however, we get 5, which is an unreasonably large probability. If we rewrite the odds as 0.6 : 0.4, we've preserved the same proportions, but made the terms sum to 1. We therefore calculate that Hamilton has a 60% probability of winning the election.
We normalized those odds by dividing each of the terms by the sum of terms, i.e., went from 3 : 2 to