There ain't No Such Thing as a Free Lunch (Controversy of Arbitrage Opportunity)

“There ain't no such thing as a free lunch.”

Robert A. Heinlein, The Moon is a Harsh Mistress

Arbitrage Opportunity

Arbitrage opportunity as "the opportunity to buy an asset at a low price then immediately selling it on a different market for a higher price." If I can buy an asset for $5, turn around and sell it for $20 and make $15 for my trouble, that is arbitrage. The $15 I gain represents an arbitrage profit.
Arbitrage profits can occur in a number of different ways.

Suppose Walmart is selling the DVD of Shaft in Africa for $10. However, I know that on eBay the last 20 copies of Shaft in Africa on DVD have sold for between $25 and $30. Then I could go to Walmart, buy copies of the movie and turn around and sell them on eBay for a profit of $15 to $20 a DVD. It is unlikely that I will be able to make a profit in this manner for too long, as one of three things should happen:

1. Walmart runs out of copies of Shaft in Africa on DVD
2. Walmart raises the price on remaining copies as they've seen an increased demand for the movie
3. The supply of Shaft in Africa DVDs skyrockets on eBay, which causes the price to fall.

This kind of arbitrage is actually quite common on eBay. Many eBay sellers will go to flea markets and yard sales looking for collectibles that the seller does not know the true value of and has priced much too low. They will buy the rare collection of Colecovision games from the yard sale for $10 then turn around and sell them on eBay for $100. There are costs to this however. First of all, you don't find rare Colecovision games just lying around, you have to spend time and energy looking for them. Secondly, you have to spend time learning what is valuable and what is not valuable so you don't find out later what you thought was worth $100 is only worth $5. Lastly, just because something has sold for $100 in the past does not mean it will sell for $100 again in the future. So given both the financial costs and the opportunity costs involved, we would expect arbitrageurs on this market to make as much money as they would doing other productive activities that require the same set of skills.

No Arbitrage Opportunity

Arbitrage is basically buying in one market and simultaneously selling in another, profiting from a temporary difference. This is considered risk-less profit for the investor/trader.

Here is an example of an arbitrage opportunity. Let's say you are able to buy a toy doll for $15 in Tallahassee, Florida, but in Seattle, Washington, the doll is selling for $25. If you are able to buy the doll in Florida and sell it in the Seattle market, you can profit from the difference without any risk because the higher price of the doll in Seattle is guaranteed.

In the context of the stock market, traders often try to exploit arbitrage opportunities. For example, a trader may buy a stock on a foreign exchange where the price has not yet adjusted for the constantly fluctuating exchange rate. The price of the stock on the foreign exchange is therefore undervalued compared to the price on the local exchange, and the trader makes a profit from this difference.

If all markets were perfectly efficient, there would never be any arbitrage opportunities - but markets seldom remain perfect. It is important to note that even when markets have a discrepancy in pricing between two equal goods, there is not always an arbitrage opportunity. Transaction costs can turn a possible arbitrage situation into one that has no benefit to the potential arbitrager. Consider the scenario with the toy dolls above. It would cost you a certain amount per doll to get the dolls from Florida to Seattle. If it costs $11 per doll, the arbitrage opportunity has been erased. 

Sources:
What is Arbitrage?
What is arbitrage?