Clergy was one way for nobility to put their offspring in, let's take for example Bernhard de Clairvaux, (1090-1153), abbot of Cluny. During the blossom of the cluniacensic reform, lots of donations reached the monasteries of Cluny and Moissac. But how did this provide them with power and what kind of power was that over whom? What else were sources of power for monasteries?
Rich monasteries in this period basically functioned like noble house: they had lands, with people who paid to live on them, they had knights that they sent periodically to the kind, etc. For example, in the Chronicle of Bury St. Edmunds (12th century), the abbot talks about himself as one of the barons, and is responsible for administering the abbey's lands.