Paper trading, or virtual trading as some like to call it, is the process of using fake money to play in the stock market. In other words, the user can buy and sell stocks, but no money is ever being risked.
Paper trading has no impact on the actual market, so users can continually execute trades and practice strategies without having to worry about losing their own money.
It is increasingly getting popular for stock brokers to offer some sort of paper trading feature within their services. Discount broker like Zecco offers paper trading for both stocks and forex.
Wall Street Survivor is a popular free paper trading platform that allows users to practice and tweak trading strategies.