Toasting doesn't just give bread a browned flavor. If the bread is stale, it temporarily improves its texture by softening the starch granules. The granules loosened and expanded in baking and have been contracting ever since the bread left the oven, gradually stiffening it. When the heat of toasting brings the granules to the point of gelatinization, what moisture remains in the bread moves in and briefly softens them.
But what about that idea of toasting a person? Why do we call the act of dedicating a sip of an alcoholic beverage "toasting"?
It comes from the medieval practice of adding a bit of toasted bread to wine -- particularly to wine flavored with spices -- to improve its flavor. (Toasted bread was an important ingredient in medieval cookery; many sauces were based on it.)
You might think that people drank to the health of somebody with "toast wine" and that's how the sense of toasting a person came about, but it actually happened in the reverse way. The toast added flavor to the wine, and the idea was that when you spoke an honored person's name over the wine, it was as if the name added flavor to the wine in the same way. "You're the 'toast' of our party" was the idea.
Only long after that did "a toast" come to mean the act of dedicating a drink.