How does 'give it up for ...' mean 'clap for ...'?

Solution 1:

From PhraseFinder:

Reference 1:

First use ... was by Arsenio Hall, who made it into a bit of a catch phrase on his television show that began in January 1987. There may be earlier usages.

... Arsenio was the first to use the catchphrase in a widely seen television show; but a great many people would have heard him use it before then, ..., about 1980 ..., when he was on tour with Gladys Knight. It simply means "Don't hold anything back," and he showed by gesture that he meant applause.

Reference 2:

Give it up -- let yourself go. Mainstream 1960s. "Flappers 2 Rappers: American Youth Slang" by Tom Dalzell (Merriam-Webster Inc., Springfield, Md., 1996) Flappers 2 Rappers says in mid-1970s it became a Hip-Hop and Rap term meaning "to express greeting, to applaud."

Reference 3:

Marvin Gaye, 1977, Got to Give it Up. Lyrics at http://marvin-gaye.guidechart.com/got-to-give-it-up.php

"giving it up" means "to applaud". "clapping" is a form of applause. Hence, "giving it up" for someone can mean clapping for him / her.

Solution 2:

Quite simply, the 'it' in question is Applause. Audiences who do not applaud are often referred to as 'stingy' or withholding of their applause, so when asked to 'give it up' for a performer, they are being asked to provide their applause - i.e. to clap.