Arbitrage is the simultaneous buying and selling of securities, currency, or commodities in different markets in order to take advantage of differing prices for the same asset. The role of arbitrageurs (individuals who engage in arbitrage) is essential for an AMM to operate and aid to keep the price the same across all exchanges.
A very basic example of this would be if you lived in a town that grew lots of apples. Due to the abundance of apples, the cost is 4 for a dollar. A few towns over doesn't grow as many apples, so the cost is 2 for a dollar. You decide to make money by purchasing them in your town and selling them for a better price at the other town. You have just engaged in arbitrage. Purchasing one asset from one market, in order to make a profit selling the same asset in another market.