As Dr. Anders likes to give the example I’ll put it here. Say you live in a house where your father has said not to throw the ball in the house. You throw the ball anyway and end up breaking the window. Your father knows you broke the window and when you go to him and say sorry he forgives you and your personal relationship is restored because you have acknowledged you did wrong and have done so with contrition. This is the repairing of the relationship between an individual and God that happens in the sacrament of Reconciliation.
However, even though the father and child have restored their relationship there’s still a broken window that exists and the mess from that which needs to be cleaned up. That would be the representation of the temporal aspect of sin. Because we are all each individuals with free will, it would not be good for us a moral agents to just wave a hand have the window be repaired. Can it happen? Yes, and that is a great mercy from the father in this scenario. Usually, as moral agents who can exercise our free will with the help and guidance of the father will make an effort to clean up the broken glass, asking for help when we need more assistance, and such of the window and work to replace it. That’s what the penance would be for; to clean up the broken glass. Sometimes people die with the relationship restored but there’s still a broken window or some broken glass on the floor, and that would be what Purgatory is for; to finish up cleaning up the remnants of the broken window since there’s no problem with the father/child relationship.
Indulgences are kinda hard to fit into the analogy though maybe someone can find the words better than me and make it work. I’ve heard Dr. Anders say it would be like if a sibling comes by and helps with the cleanup so it makes the time of the temporal affect shorter or go away entirely. I don’t quite like that extension to the analogy because it seems a bit off to me though I can’t quite place my finger on why. Plenary and Partial indulgences differ in the amount of temporal punishment they remove due to past confessed and absolved sins. Plenary indulgences remove all temporal punishment and partial indulgences remove only part of the punishment. Usually they are gained through prayers, actions (such as reading scripture, making a pilgrimage, going to mass on certain days, etc.), and most importantly not being attached to sin. The action of getting the indulgence either for yourself or for others is supposed to draw you close to the Lord and be done out of love.
I hope that helps a bit. As always, analogies can only get a person so far. You make amends for temporal punishment by living the Gospel and loving the Lord with all your heart, with all your soul, and with all your mind. Walk firmly with Him and love Him. Turn back to him in sincerity when you fall, because you probably will fall again. Simple words, but hard to do.
I really do like to read all this topics and that’s the reason I’ve joined here