A systematic error is an experimental error which systematically skews results; that is, on average it will produce results which are either higher or lower than the variable which is supposedly being measured. A classic example of a systematic error is a zero error on a measuring device - for instance, scales which report a weight even when there is nothing on them. Systematic errors can also result when the experimenter fails to take into account all the factors influencing their results: A systematic error in an experiment looking at heat transfer could be caused by failing to take into account all possible heat sinks and sources, for example.
Demographic statistics are especially vulnerable to systematic errors, because it can be so hard to eliminate the effects of one factor - like poverty - when looking at some related area, such as crime. This is of great concern in epidemiological studies, where there is often strong correlation between different lifestyle factors which may affect the results - for example, the lower rates of heart disease in southern Europe may be down to their consumption of red wine, as was widely believed at one time (and which may indeed be the case); they may be the result of greater olive oil consumption in that part of the world; or they may be due to some other factor, like exercise. The contribution of all these strands must be carefully picked apart to avoid a systematic error in the assessment of any one.
Systematic error is contrasted with random error, which throws the results off evenly in both directions; where a systematic error remains however many runs of an experiment you perform, systematically skewing the results, random errors reduce an experiment's precision but tend to cancel out with enough runs, eventually leaving the mean result very close to what it should it should be. Since it is not possible to use repetition to avoid skewed results from systematic errors, experimenters must instead work hard to reduce their contribution, and identify as well as they can the size and nature of any that they cannot eliminate entirely.
Mostly remembered from physics lectures; http://trochim.human.cornell.edu/kb/measerr.htm was the single best web page about experimental errors that I could find.