Observed in cool chromospheric lines, such as Hα or Ca II H, coronal rain corresponds to cool and dense plasma falling from coronal heights. Considered as a peculiar sporadic phenomenon of active regions, it has not received much attention since its discovery more than 40 years ago. Yet, it has been shown recently that a close relationship exists between this phenomenon and the coronal heating mechanism. Indeed, numerical simulations have shown that this phenomenon is most likely due to a loss of thermal equilibrium ensuing from a heating mechanism acting mostly toward the footpoints of loops. We present here one of the first high-resolution spectroscopic observations of coronal rain, performed with the CRisp Imaging Spectro Polarimeter (CRISP) instrument at the Swedish Solar Telescope. This work constitutes the first attempt to assess the importance of coronal rain in the understanding of the coronal magnetic field in active regions. With the present resolution, coronal rain is observed to literally invade the entire field of view. A large statistical set is obtained in which dynamics (total velocities and accelerations), shapes (lengths and widths), trajectories (angles of fall of the blobs), and thermodynamic properties (temperatures) of the condensations are derived. Specifically, we find that coronal rain is composed of small and dense chromospheric cores with average widths and lengths of 310km and 710km, respectively, average temperatures below 7000K, displaying a broad distribution of falling speeds with an average of 70kms-1, and accelerations largely below the effective gravity along loops. Through estimates of the ion-neutral coupling in the blobs we show that coronal rain acts as a tracer of the coronal magnetic field, thus supporting the multi-strand loop scenario, and acts as a probe of the local thermodynamic conditions in loops. We further elucidate its potential in coronal heating. We find that the cooling in neighboring strands occurs simultaneously in general suggesting a similar thermodynamic evolution among strands, which can be explained by a common footpoint heating process. Constraints for coronal heating models of loops are thus provided. Estimates of the fraction of coronal volume with coronal rain give values between 7% and 30%. Estimates of the occurrence time of the phenomenon in loops set times between 5 and 20hr, implying that coronal rain may be a common phenomenon, in agreement with the frequent observations of cool downflows in extreme-ultraviolet lines. The coronal mass drain rate in the form of coronal rain is estimated to be on the order of 5 × 109gs-1, a significant quantity compared to the estimate of mass flux into the corona from spicules.