Well, first of all, let me point out that Mother Teresa, while a Saint, isn’t the Magisterium of the Church. So, her expressions of the faith may or may not be on target, or as well formulated as they should be. That doesn’t detract from her sainthood, though, in any way.
That being said, here’s how the process works:
When we sin, we are due at that time, some temporal punishment, due to justice.
When we repent, go to Confession, and given absolution, we are forgiven our sins, and cannot be sent to hell for the commission of those sins we confessed.
However, we are still due some temporal punishment. The priest gives us penance during our Confession, which may mitigate some or all of our temporal punishment. If it does not, we still “owe” that temporal punishment, because of justice.
Everyone in Purgatory makes it to heaven. That means God has forgiven them their sins. Otherwise, they wouldn’t be able to make it into heaven.
If I had to give a simple example, I would point to an incident I had as a small boy. We were visiting a friend of my father’s. I was playing baseball with the family children, and we were just getting ready to leaven, so I wanted one more at bat. My father cautioned against hitting the ball too hard because I might break a window. I assured him that I couldn’t hit it that far, and swing as hard as I could at the next pitch. Guess what? I could hit it that far, and broke a window! I was sorry, and apologized to Mr. Bob (the owner and family friend). But I still owed him for the window, to satisfy justice. My father paid him for the window and I worked it off cutting grass to pay my father back. Justice was satisfied, even though as soon as I apologized, Mr. Bob forgave me.