If you’re seeking deliverance, you want to be set free or removed from a bad situation. If you're taken hostage in a bank heist, you might pray for deliverance.
You probably notice that deliver makes up a big chunk of deliverance. One meaning of deliver is “to set free” — and that’s what deliverance is: the act of setting someone free. Deliverance often has religious connotations, but the word can be used for other kinds of rescue or liberation. You might want deliverance from the hardship of working on your uncle’s farm all summer, or at least deliverance from the smell of manure.