ARIMA as an acronym for Autoregressive Integrated Moving Average Model (also known as Box-Jenkins model). It is a class of models of random processes in discrete time or time series. ARIMA model is widely used in time series analysis.
ARIMA model extends the autoregressive moving average (ARMA) model. In contrast to the ARMA model, which is adequate only for stationary time series, ARIMA model may be an adequate model for nonstationary time series. In a few words, the essence of ARIMA is to apply the ARMA model not immediately to the time series at hand, but after its preliminary differencing (differencing means using the differences between consecutive values instead of the values themselves).