When you have a broker and are buying or trading shares, you get to order them around or give them instructions about what and when to buy (and sell).
There are different flavors of orders. A market order means you're asking your broker to buy a certain amount of a certain security at the current market price. The idea is that the broker is expected to buy or sell now, but the trick is that some securities will go up and down in price a lot, so the price you think you're selling for might not end up being the price the broker can get for you.
Example
Ellen calls her broker and says, "Gimme 1,000 shares of Coke at market." The broker looks at her screen and says, "Okay, KO is trading at $68.42." That's how much Ellen pays per share.