It's like a grown-up, sophisticated version of "let's pretend". Or, if you prefer, it's like being on a movie set with no script, where you’re the protagonist, and the outcome is determined by the choices and actions of the players.
But, as is known, a video is worth a thousand words! This short video (by Court of Moravia, a Czech larp group) shows very clearly, in about 2 minutes, what’s a Live Action Role-Play and how does it work. If you haven’t watched it yet, do it and it will dispel any doubt you might have! (just turn on the subtitles, unless you speak Czech).