A limit order is one that is given with a price limit.
An investor wishing to buy or sell securities places a limit order for a certain number of shares at a certain price. A buyer will set a maximum price, a seller will set a minimum price.
A limit order is valid for a certain lifetime, after which it expires.
If a limit order is matched against another limit order at a different price (e.g. a buy at 100p can match a sell at 99p), then the market's trading rules will determine which price the trade takes place at.
In most markets a limit order may be partly filled, if there are insufficient shares available/asked for within the price limit. There are other (less commonly used) order types for investors who wish to trade only certain minimum quantities etc.
Limit orders are widely used for dealing in shares that trade through matched bargain systems. They are less useful for share that trade through market makers although they are still useful for investors who want to buy only if the price falls or sell only if the price rises.
Private investors investing in reasonably liquid securities will usually find the convenience of a market order preferable.