An outlier is a single data point that goes far outside the average value of a group of statistics. Outliers may be exceptions that stand outside individual samples of populations as well. In a more general context, an outlier is an individual that is markedly different from the norm in some respect.
Outliers are an important factor in statistics as they can have a considerable effect on overall results. In especially small sample sizes, a single outlier may dramatically affect averages and skew the study's final results.
An outlier can happen due to disinformation by a subject, errors in a subject's responses or in data entry. In some cases, it's clear that outliers should be removed as errors. In others, it may come down to standards or judgment calls where outliers are a natural deviation.
Statisticians, who often attempt to mitigate the effect of outliers, have come up with ways to identify what makes an outlier. For example, in a scatter plot where data points are graphed, outliers are visually identifiable. In a box plot, outliers are found by using equations to find if they exceed defined norms.
Outliers can sometimes indicate errors or poor methods of sample gathering. They can also indicate an anomaly or something of interest to study since it's not always possible to determine if outliers are in error. Although the effects of outliers can skew results of statistics, it is rare that they are entirely removed from results without observations.