Outliers are values in the data that are outside the range of what is to be expected. "What is to be expected?" is of course subjective. Some people will define an outlier as anything beyond three standard deviations of a normal distribution, or anything beyond 1.5 times the interquartile ranges. This, of course, may be good starting points, but there are many examples of real data that defies any statistical explanation. These rules of thumb are also highly dependent upon the form of the data. What might be considered an outlier for a normal distribution would not hold for a lognormal or Poisson distribution.
In addition to potential single variable outliers, outliers can also exist in multivariate form, and are more prevalent as data is examined more closely in a high-dimensional space.
Whenever they appear, outliers should be examined closely since they may be simple errors or provide valuable insight. Again, it is best to consult with other collaborators when you suspect deviation...
