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What does the phrase"sign up for" mean?Could you please tell me?
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When you joined this site, you signed up for it. It means to give your name and information (possibly a fee) to join/start a service.

The use of "sign" comes from "signing your name".
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Search for idioms (or phrasal verbs) here:
http://www.answers.com/library/Idioms
Search with
sign
in this case