A fairly close synonym for "camp" would be "effeminate". It is generally applied to a man who is doing something in a lady-like way. It is often used to describe the way a (stereotypical) homosexual man walks or talks, and might also apply to his hand gestures.
"Camp" can also describe the way someone dresses - for example, some well-known British homosexual celebrities such as Graham Norton and Julian Clary dress in a camp way when they appear on TV shows. They wear very brightly-coloured clothes, often made of shiny material. Do a search for them on Google Images and you will see what I mean!
I think the UK and US versions of the word have developed different meanings. I don't know anything about the origins of the term, but it definitely has more effeminate connotations over here! I'm sure the possible meanings extend beyond this, though.
I've also heard it used in a theatrical context -- an actor using unnecessary or exaggerated gestures/expressions, or doing bits of business (performing actions) that had nothing to do with the character or the scene.
A camp character in the American TV show "The Simpsons" (Homers Phobia 4F11) who was gay and had a shop containing kitsch nostalgia, wore bowlng shirts, this combines both the US "camp" meaning "tacky, kitsch" and the UK version..."affected and effeminate". Oh, and Marge, who prefered to skirt the issue of his homosexuality refered to him as "festive". There is an expression in UK English "as camp as a xmas tree".