The adv finally has 3 senses (first 3 from tagged texts)
1. (45) finally, eventually, at length -- (after a long period of time or an especially long delay; "at length they arrived")
2. (20) last, lastly, in conclusion, finally -- (the item at the end; "last, I'll discuss family values")
3. (20) ultimately, finally, in the end, at last, at long last -- (as the end result of a succession or process; "ultimately he had to give in"; "at long last the winter was over")