Systematic trading is a way of defining trade goals, risk controls and rules that can execute trade orders in a methodically way.
Thanks to the methodically approach, rules can be tested using past data.
It does not need to include the use of computers, but is almost impossible to achieve trading goals without using a computer and a systematic trading system in which rules are programmed. Systematic traders employ technology to capture profit opportunities.
The opposite is discretionary trading. Compared to systematic trading, discretionary trading has more influence from emotions, no easy possibilities of backtesting and a limited risk control
Similar ideas are algorithmic trading and quantitative trading. But algorithmic trading is more related to how to trade an order or a set of orders, using a set of well-known algorithms. Quantitative trading includes all those kind of trading (systematic, discretionary, algorithmic, HFT...) which uses too quantitative techniques to decide trading options and executions.
Some links:
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http://www.adaptrade.com/Articles/article-sys-prof.htm
http://www.adaptrade.com/Articles/article-sys-start.htm
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