To make a record of having borrowed (something) for temporary use; as, to check out a book at the library; to check out equipment from a depository.
3.
To bring (items to be purchased) to a checkout counter (as at a supermarket or other retail store) where the prices may be totaled and the bill may be paid.
... an interesting semi-parallel to this term among typographers and printers: When new typefaces are being punch-cut by hand, a 'smoke test' (hold the letter in candle smoke, then press it onto paper) is used to check out new dies. ... — The Jargon File, Version 4.0.0
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