Systematic error is the error that is constant in a series of repetitions of the same experiment or observation. Usually, systematic error is defined as the expected value of the overall error.
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