Observations in a data set which exert a large influence on estimates produced by regression analysis.
(Paul Grootendorst, PPG2010)
For example, consider an ordinary least squares (OLS) regression. The OLS parameter estimator is a weighted average of n observations on outcome variable y. Given that it is a weighted average of n values of y, and the weights differ by observation, some observations will have more influence on OLS estimates than others.
Statistical software can be used to identify the observations which exert the most influence on a particular regression coefficient. It can be useful to identify the most observations and to re-run regression analysis with and without them included. If the two estimates differ significantly, it may mean that your regression is sensitive to outliers. The possibility of data entry error should also be considered if extremely influential observations are detected, and these observations should be examined closely to ensure that data has been entered into the database correctly.