After-hours trading is defined as the exchange of securities outside of an exchange's specified regular trading hours (usually 9:30 AM to 4 PM Eastern). After-hours trading occurs through an electronic communication network (ECN), which is essentially an interface that allows buyers and sellers to match up their buy and sell orders for a security even though the regular exchange through which the security trades is closed for the evening.
While there are many benefits of after-hours trading, one of its drawbacks is that it usually operates with significantly less volume than the traditional exchange-based trading day. It is because of the low volumes typically traded through after-hours trading systems that the after-hours bid and ask prices for specific securities can become widely separated.
This may seem like a difficult concept to understand, but it is actually quite straightforward. Recall that securities are traded through exchanges by creating a match between buyers and sellers. For example, the "quote" for a stock you see is really just the last price at which a trade was successfully completed. Also recall that the "bid" for a security is the buy order with the highest price that has not yet been filled, and the "ask" for a security is the lowest-priced sell order that has not yet been filled.
In order to match the hordes of buy and sell orders, exchanges start with the highest bid (buy order) and try to match it up with the lowest ask (sell order). Because there are usually thousands of bid and ask orders in the system during the trading day, chances are usually very good that there will be little difference separating the highest bid order from the lowest ask order. However, once the trading day finishes and after-hours trading commences, there are drastically fewer participants entering bid and ask orders into the system for a security. Because of this lack of order volume, there is a much greater chance that a big dollar value difference will exist between the quoted bid and ask values for a particular security.
If a stock has a wide difference between its after-hours bid and ask prices, this usually means there is little (if any) after-hours trading going on, and usually does not imply there has been a big change in the security's market value.
To learn more about the mechanics of securities trading, check out "The Basics of Trading a Stock: Know Your Orders."