An example of systematic error is an electronic scale that, if loaded with a standard weight, provides readings that are systematically lower than the true weight by 0.5 grams - that is, the arithmetic mean of the errors is -0.5 gram.
The opposite (complementary) concept is random error.
From practical standpoint, systematic errors are usually much more serious nuisance factors than random errors - because their magnitude cannot be reduced by simple repetition of the measurement procedure several times.
An additive systematic error is named bias.
See also the short courses