To confirm and pay for goods and services at a facility (e.g.: supermarket, online store, hotel) when leaving.
Be sure to check out of the hotel before noon.
To withdraw (an item), as from a library, and have the withdrawal recorded.
He checked his favorite mystery out for the twenty-third time.
To record (someone) as leaving the premises or as taking something therefrom, as from a library or shop.
The desk clerk checked out the family that had been staying in room 322.
To examine, inspect, look at closely, ogle; to investigate; to gather information so as to make a decision.
Check it out! Best prices in town.
To obtain source code from a repository.
To become uninterested in an activity and cease to participate in more than a perfunctory manner; to become uncooperative.
To become catatonic or otherwise nonresponsive.
To leave in a hurry.
(by extension) To die.
To prove (after an investigation) to be the case, or to be in order.
The first two leads check out; I'll assume the third one is also valid.