Offset is a variable which used in Poisson Regression Analysis. This analysis is used whenever the data is recorded over an observed period. Eg: Number of Customers who arrive at a restaurant in one hour, Number of trees in a square unit area. Here the data is measured under a pre determined period (exposure) rather than absolute numbers (count). Thus Poisson regression is used when the data is rate based (count divided by exposure).
Offset is the variable that is used to denote the exposure period in the Poisson regression. Let us consider the simple linear regression equation given below:
To put it in simple terms, offset variable is the log of the time period under study and has a regression coefficient of 1.