We present a stellar population analysis of the absorption line strength maps for 48 early-type galaxies from the SAURON sample. Using the line strength index maps of Hβ, Fe5015 and Mgb, measured in the Lick/IDS system and spatially binned to a constant signal-to-noise ratio, together with predictions from up-to-date stellar population models, we estimate the simple stellar population-equivalent (SSP-equivalent) age, metallicity and abundance ratio [α/Fe] over a two-dimensional field extending up to approximately one effective radius. A discussion of calibrations and differences between model predictions is given. Maps of SSP-equivalent age, metallicity and abundance ratio [α/Fe] are presented for each galaxy. We find a large range of SSP-equivalent ages in our sample, of which ~40 per cent of the galaxies show signs of a contribution from a young stellar population. The most extreme cases of post-starburst galaxies, with SSP-equivalent ages of <=3Gyr observed over the full field-of-view, and sometimes even showing signs of residual star formation, are restricted to low-mass systems (σe <= 100kms-1 or ~2 × 1010Msolar). Spatially restricted cases of young stellar populations in circumnuclear regions can almost exclusively be linked to the presence of star formation in a thin, dusty disc/ring, also seen in the near-UV or mid-IR on top of an older underlying stellar population. The flattened components with disc-like kinematics previously identified in all fast rotators are shown to be connected to regions of distinct stellar populations. These range from the young, still star-forming circumnuclear discs and rings with increased metallicity preferentially found in intermediate-mass fast rotators, to apparently old structures with extended disc-like kinematics, which are observed to have an increased metallicity and mildly depressed [α/Fe] ratio compared to the main body of the galaxy. The slow rotators, often harbouring kinematically decoupled components (KDC) in their central regions, generally show no stellar population signatures over and above the well-known metallicity gradients in early-type galaxies and are largely consistent with old (>=10Gyr) stellar populations. Using radially averaged stellar population gradients we find in agreement with Spolaor et al. a mass-metallicity gradient relation where low-mass fast rotators form a sequence of increasing metallicity gradient with increasing mass. For more massive systems (above ~3.5 × 1010Msolar) there is an overall downturn such that metallicity gradients become shallower with increased scatter at a given mass leading to the most massive systems being slow rotators with relatively shallow metallicity gradients. The observed shallower metallicity gradients and increased scatter could be a consequence of the competition between different star formation and assembly scenarios following a general trend of diminishing gas fractions and more equal-mass mergers with increasing mass, leading to the most massive systems being devoid of ordered motion and signs of recent star formation.