Is basically a middle-man which safeguards your transaction when you're trading with unknown/untrusted people.

An example:

You want to sell 1 BTC to someone.

1. You send 1 BTC to LocalBitcoins.
2. They hold your 1 BTC while the buyer does the money transaction (deposit/wire/etc...).
3. When you confirm you received the money, you tell LocalBitcoins to release the coins.
4. They send the 1 BTC to the seller.

So, LocalBitcoin is acting as the escrow. You <> LocalBitcoins <> Buyer.

This way, you can't run with the buyer money if he sends first (since the 1 BTC is with the trusted middle-man, which is LocalBitcoins), and neither he can run with your 1 BTC if you send first (because they are only released to the buyer after the wire).