Etymology
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back up (v.)

1767, "stand behind and support," from back (v.) + up (adv.). Meaning "move or force backward" is by 1834. Of water prevented from flowing, by 1837.

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Definitions of back up

back up (v.)
give moral or psychological support, aid, or courage to;
Synonyms: support
back up (v.)
move backwards from a certain position;
Synonyms: back off / back down
back up (v.)
establish as valid or genuine;
Can you back up your claims?
Synonyms: back
back up (v.)
make a copy of (a computer file) especially for storage in another place as a security copy;
You'd better back up these files!
back up (v.)
become or cause to become obstructed;
Synonyms: clog / choke off / clog up / congest / choke / foul
From wordnet.princeton.edu