Auto-regressive parameters use previous values of the time series to help predict the next value for the series. The Auto-regressive order of an ARIMA model is closely related to the Partial Autocorrelation function (PACF). Further reading on this concept is available here.

Differencing a time series entails subtracting the previous value in the series from the current value of the series. In practice, it is used eliminate some types non-stationarity that can be present in the series. Further reading on the differencing (backshift/lag) operator is available here. You can also read about how to determine if your time series requires differencing in Rob Hyndman's book Forecasting Principles and Practice.

Moving Average parameters use the shocks, or error terms, of a previous value in the series to help predict the next value of the series. The MA order of an ARIMA model is closely related to the Autocorrelation function (ACF). Further reading on this concept is available here.