What political power did the Church have over people in the medieval times?

I would say that the Catholic Church had political power
over people in the Middle Ages in a few different
ways.

First of all, there were places that were directly
under the control of the Church -- places where the Pope was the official ruler of the
country.  This was in the Papal States in what is now
Italy.

Second, the Church owned a lot of land in other
parts of Europe.  Each monastery, for example, owned lots of land and the abbots of the
monasteries ran those lands.  The people on the land (if they were serfs) belonged to
the monastery.  In that way, the Church had political power because it had temporal
power over its estates.

Finally, the Church had moral
authority that could be used politically.  The Church was seen as the only way to Heaven
and so the clergy could be pretty important in making people behave in certain ways. 
They could threaten, for example, to excommunicate people who did not make the "right"
choices. 
This gave the Church more power of an indirect
sort.