My simple definition of systematic trading is a system, whose trading rules are based on quantifiable results. Whether the system is automated or mechanical from an execution standpoint is irrelevant.
Below is an example of how a systematic trader and discretionary trader differ in their approach.
The systematic trader approach
A systematic trading system would say for example, when the 20MA crosses the 50MA, 71% of the time stock XYZ rallies 4.25%. So the system would buy stock XYZ and set a profit target of 4.25%. 71% of the time the trade "should" win and 29% of the time the trade "should" lose. It's not a guarantee but a highly probable and calculated trade.
The discretionary trader approach
Using the same example, a discretionary trader, someone who is non-systematic would say, I've seen in the past when the 20MA crosses the 50MA, stock XYZ often rallies a lot. But they don't know if "often" means the probability is high enough to take the trade and how to define "a lot" in terms of setting a profit target.
Notice how the systematic trader approaches the problem methodically. A trade is only taken when probability is favorable and profit targets are not randomly set but based on historical price action.
I previously owned a retail store. After a few years I invested in a point of sale (POS) software system. Sales reps would ask how a certain product is selling. In the past I may have answered awesome, because yesterday I sold two. But the POS would perhaps say 9% sell through because prior to those two sold yesterday, I hadn't sold any in a month.
The point being, as humans we often form opinions biased by recent events. Whereas a computer does not form any opinion, but rather uses real data over an extended period of time.