What it is:
An arbitrageur is a person who exploits the differences in the price of a given security by simultaneously purchasing and selling that security.
How it works/Example:
For example, if Company XYZ's stock trades at $5 per share on the New York Stock Exchange and the equivalent of $5.05 on the London Stock Exchange, an arbitrageur would purchase the stock for $5 on the NYSE and sell it on the LSE for $5.05, pocketing $0.05 per share. Theoretically, the prices on both exchanges should be the same at all times, but opportunities arise when they're not.
Arbitrageurs also try to exploit price differences created by mergers. In some cases, they purchase the of companies that are the targets of purchase offers, hoping to pocket the difference between the trading price and the eventual payment resulting from the merger. In theory, arbitrage is a riskless activity, but merger arbitrage is not riskless - -there is a chance the merger not happen, and the price of the target's would probably fall in that event.
Why it matters:
Institutions are usually the biggest arbitrageurs -- the large volumes of transaction costs that would normally eliminate any individual investors could hope for are often relatively minimal for institutions.
The main creator of opportunity used to be a lack of real-time communication about prices in other markets, but technology has reduced the number of opportunities. The relatively few opportunities that do exist are elusive and don't last for long -- when people realize that a security is cheaper on one exchange than another, their interest in exploiting the opportunity drive up the price of the "cheap" security and drive down the price of the "expensive" security until there is no longer a price difference. In a sense, arbitrageurs ensure equilibrium in the markets.