Posterior probability is a concept that occurs in Bayesian probability theory. You can read about it on this Wikipedia page. In this theory, it is often convenient to take the logarithm of the probability. Since a probability is less than 1, its logarithm is negative. So, again as a matter of convenience, it is usual to deal with the negative of the logarithm. That gives you the "negative log posterior".

The abbreviation "Pr" almost always stands for "probability".