We aren't told directly whey the monk is on the trip. He manages the Prioress's estate so, since she is on the trip accompanied by some other priests and nuns, he is part of that entourage. His real reason for going, however, is probably for the adventure and perhaps the chance to do some hunting. We are told in the GP that the monk likes to hunt and devotes more time and energy to that undertaking than he does to his religious duties. When the monk tells his tale, which is actually a series of short tales about other prominent figures and their falls from greatness, he does so somewhat pompously. His words before he launches into the tales tell us that. So perhaps another reason for his attendance on this trip is that he feels he is of high social stature and this is the thing to and the place to be seen.