An autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. Typically, these models are fitted to time series data to predict future data points (forecasting).
An ARIMA model adds to an ARMA model a degree of differencing, which makes the time series stationary, if necessary. To make the time series stationary, an ARIMA model uses both differencing and nonlinear transformations, such as logging.
A random variable that is a time series is stationary if its statistical properties are constant over time. An ARIMA model acts as a filter that separates the signal from the noise, so that only the signal is used for forecasting.