The letters refer to the different “orders” that the priest or sister belong to. For example:
Fr James Martin, S.J. : S.J. stands for Society of Jesus which is the formal name for the Jesuits. So Fr Jim would be a Jesuit priest.
Fr David Dwyer, C.S.P.: C.S.P. stands for Community of St Paul which is the formal name for the Paulists. So Fr Dave is a Paulist Father.
Sr. Christine Wilcox, O.P.: O.P. stands for Order of Preachers which is the formal name of the Dominicans. So Sr. Christine is a Dominican Sister.
As you can see sometimes the letters stand for what the order’s charism is as it does for the Dominicans who have a central mission regarding preaching.
Now I know what your next 2 questions will be:
1) How do you know what all the orders’ “letters” are?
Well some you just start to see more often and you’ll memorize them. But occasionally, you’ll see one that is unfamiliar. Priests and Nuns are quite used to that and they enjoy telling people what their particular order is all about so don’t be afraid to ask them what order they come from. Cardinal George from Chicago has O.M.I after his name and he’ll be glad to tell you all about the Oblates of Mary Immaculate if you give him the chance.
2) What if they don’t have any letters after their name?
Then, most likely, they are a diocesan priest–which means that they haven’t joined a particular religious community or an order but instead, chose to join the diocesan priesthood. Diocesan priests tend to simply be responsible for the administration of parishes and schools in a particular geographic area (known as a diocese). “Order” priests usually serve in a parish church as well but their main focus is not on the parish’s administration but on the charism of their founder. For example the Jesuits are educators so they build a lot of schools and universities. Franciscans work with the poor so they wear a simple brown robe and give away their belongings and open soup kitchens and homeless shelters. Etc. Sometimes communities break off from other communities. Like there are a bunch of different types of Franciscans…they all follow St Francis as the one who inspired them, but they all might have slightly different approaches as to how they do that.