What does "after all" mean?

Despite everything, nevertheless, as in The plane took off half an hour late but landed on time after all.

After everything else has been considered, ultimately, as in Mary has final approval of the guest list; after all, it's her wedding. The two usages are pronounced differently, the first giving stress to the word after and the second to the word all. Both date from the early 1700s. Also see when all is said and done.