LARP stands for Live Action Role Playing. That's what most LARPers will agree on. It is interactive improvisation between people who are each playing a persona. After that, ask ten different LARPers what they think LARP is, and you may get twelve or thirteen different answers!
That's because there are all sorts of games and players. LARP is not solely medieval fantasy games, or dark games filled with vampires, or mysteries where everyone tries to find out who did it, or games where people wear armor and beat on each other with padded weapons, or...
LARP is all of these, and more.
There are some things in common amongst all of these games. Everyone at the game comes in character. You play a role, like the Russian ambassador to Germany, the drummer from the band Toxic Waste, or the doctor on board a luxury starliner. For the duration of the game, you dress, speak, act and live the part. You've got an agenda for the game - a list of things that you must accomplish. Some tasks are easy, some things are hard. Some players may be working towards the same goals as you, while others may be working against you.
There's no script. You improvise all your lines. You don't operate in a vacuum, because you have a character description, a background history of who you're trying to be.
You're also not alone. Games can be small, with only a few characters, they can be large, with upwards of sixty or seventy players, or they can be huge. Games can last a few minutes, four, six, or eight hours, an entire weekend, or even longer, played in several sessions. A good LARP can be an amazing experience and incredibly fun to play.
Because it's fun! People roleplay for a whole number of reasons. Some for escapism because it's lots of fun to be someone else for a few hours or a few days at a time, for the social aspects of the game and the opportunity to meet new people, and for the pure exhilaration of letting your mind run wild in a world of complete fantasy. Some players of LC style games like the opportunity to get away from their desks and do something physical in the fresh air.
Yes, there are many similarities, but there are also many differences. In a tabletop game you describe what your character is doing, but in a Live Action game you do the actions your character does.