Backtesting is a method of testing trading strategies by seeing how they would have performed after the fact.
This is done by running a plan over historical price data, seeing what it would have generated, and buying and selling signals. Backtesting is essential to strategy development as it allows you to fine-tune your strategy before running it live in real markets.
Automated or algorithmic trading systems rely heavily on Back Testing because it enables you to test an approach over a large amount of historical data in a relatively short space of time.
The MT4 and MT5 platforms feature their own backtesting facility that allows you to backtest your EAs (Expert Advisors) and tweak their parameters before ever running them under live conditions.