Refers to the standard deviation of the sampling distribution of a statistic calculated from a sample. Standard errors are often required when forming confidence intervals or testing hypotheses about the population from which the statistic was sampled.
In data analysis, quantities of interest (e.g., the mean, SD, slope, or perhaps a t statistic) are calculated using sample data. Therefore, if a new sample were gathered, the statistic would differ unless the new sample were identical to the first. If samples were calculated repeatedly, the statistic would bounce around according to a probability distribution. The standard error (SE) is the standard deviation of that sampling distribution.
Knowing the SE is fundamental to many aspects of data analysis, including the formation of confidence intervals and the testing of statistical hypotheses.