The Gaia Radial Velocity Spectrometer provides the unique opportunity of a spectroscopic analysis of millions of stars at medium-resolution in the near-infrared. This wavelength range includes the Ca II infrared triplet (IRT), which is a good diagnostics of magnetic activity in the chromosphere of late-type stars. Here we present the method devised for inferring the Gaia stellar activity index together with its scientific validation. A sample of well studied PMS stars is considered to identify the regime in which the Gaia stellar activity index may be affected by mass accretion. The position of these stars in the colour-magnitude diagram and the correlation with the amplitude of the photometric rotational modulation is also scrutinised. Three regimes of the chromospheric stellar activity are identified, confirming suggestions made by previous authors on much smaller $R'_{\rm HK}$ datasets. The highest stellar activity regime is associated with PMS stars and RS CVn systems, in which activity is enhanced by tidal interaction. Some evidence of a bimodal distribution in MS stars with $T_{\rm eff}\ge$ 5000 K is also found, which defines the two other regimes, without a clear gap in between. Stars with 3500 K$\le T_{\rm eff} \le$ 5000 K are found to be either very active PMS stars or active MS stars with a unimodal distribution in chromospheric activity. A dramatic change in the activity distribution is found for $T_{\rm eff}\le$3500 K, with a dominance of low activity stars close to the transition between partially- and fully-convective stars and a rise in activity down into the fully-convective regime.