When I go to confession, after the priest absolves me sometimes he will say “For your penance, say three hail Mary’s, three Glory Be’s and an Our Father”, or something similar.
When he says “For your penance”, Is he in actual fact prescribing an indulgence?
No. What’s going on is this:
You have repented of your sins and gone to Confession. (These steps are also called contrition and confession.) The priest, in the person of Christ, has absolved you of your sins.
The next step is to show willingness to make reparation for your sins. You do this by accepting the penance that the priest gives you, and then doing it.
If you had done something like steal $100,000 of money, obviously the first reparation would be to give the money back (or as much as you can), so that would be part of your penance. If you did something like being mean to your brother, he could assign you the penance of doing nice things for him and making up with him.
In other cases, reparations are not as clear, or you have mostly sinned against God and need to make reparations to Him. The priest would then assign you a symbolic prayer or useful activity, like reading the Bible.
You don’t actually have your sins totally absolved off you until you perform your penance and thus, finish showing your willingness to make reparation. It’s like completing a covenant action. This is why priests are supposed to try to make penances very simple and definite, so that people can be sure they’re done. It’s also why you should always tell the priest if a penance will be really impossible to fulfil, either at the time or later on. If something happens to prevent carrying out a penance, go to Confession again with the same priest or another priest and explain what happened. You can get another penance.
So here’s the thing with penances. You’re not there to earn an indulgence (although, yeah, you can get a two-fer and get indulgences for yourself or the Poor Souls or some dead person you know! Bonus!). You’re praying to show God that you mean to make reparations and do penances, and to let the absolution take effect.