Local Bitcoins is a different sort of exchange that allows anyone anywhere to trade. It therefore has the largest amount of markets – although some without much liquidity – for example in Venezuela and other emerging markets. LocalBitcoins works like an open outcry with people in the same location as you – if you want to trade you can place a buy or a sell for a price and wait to be contacted by someone who wants to execute that trade. After agreeing the trade funds are released and held in escrow and depending on the specifics of the local banking system and times for transactions to get confirmed, the trade will eventually be completed.
There can be complications which mostly come in the form of couterparty risk – where someone refuses to go ahead with the trade as the price in the market has moved in their favour – so they gain by keeping the bitcoins or USD if they have gone up. Localbitcoins has a dispute resolution system in place to handle these sorts of issues – but on the flipside there is a reputation based system – so you can gauge whether your trading party is reliable or not.
Trading fees vary and depend on whether you have placed an advert to sell – whereby LocalBitcoins takes a 1% fee.
In all a good means to exchange Bitcoin but it doesn’t have the razor edge price discovery, and execution time of more traditional order driven exchanges.