The Papal Controller is a powerful honor that can be held by only one catholic nation. The country with most cardinals in the curia is the Papal Controller. The Papal Controller will gain a few bonuses including prestige and an additional diplomat.
Gaining Control of the Curia
The seven cardinals who make up the curia cannot be swayed. How does a nation gain control of the curia if the holy men can't be bribed? There are now five cardinals on the outside, waiting to get in to the curia once another Cardinal dies. These cardinals can be swayed by investing papal influence into them.
So you are, in effect, spending assets on the chance that a cardinal you support will get promoted. Of course, you don't know how much others have invested in that cardinal so you could be wasting influence, and he may not live long enough to enter the curia anyway. But we hope that the prestige and diplomatic bonus make the curia a prize you cannot entirely neglect.