By definition, capitulation means to surrender or give up. In financial circles, this term is used to indicate the point in time when investors have decided to give up on trying to recapture lost gains as a result of falling stock prices. Suppose a stock you own has dropped by 10%. There are two options that can be taken: you can wait it out and hope the stock begins to appreciate, or you can realize the loss by selling the stock. If the majority of investors decides to wait it out, then stock price will likely remain relatively stable. However, if the majority of investors decides to capitulate and give up on the stock, then there will be a sharp decline in its price. When this occurrence is significant across the entire market, it is known as market capitulation.
The significance of capitulation lies in its implications. Many market professionals consider it to be a sign of a bottom in prices and consequently a good time to buy stocks. This is because basic economic factors dictate that large sell volumes will drive prices down, while large buy volumes will drive prices up. Since almost everyone who wanted (or felt forced) to sell stock has already done so, only buyers are left - and they are expected to drive the prices up. (If you are unfamiliar with these principles, check out our Economics Basics Tutorial.)
The problem with capitulation is that it is very difficult to forecast and identify. There is no magical price at which capitulation takes place. Often, investors will only agree in hindsight as to when the market actually capitulated.
For more on this topic, check out the article Capitulation Defined.