Arima function in the forecast package is more explicit in how it deals with constants, which may make it easier for some users relative to the
arima function in base R.
ARIMA is a general framework for modeling and making predictions from time series data using (primarily) the series itself. The purpose of the framework is to differentiate short- and long-term dynamics in a series to improve the accuracy and certainty of forecasts. More poetically, ARIMA models provide a method for describing how shocks to a system transmit through time.
From an econometric perspective, ARIMA elements are necessary to correct serial correlation and ensure stationarity.