K2 was the name of a mission reusing the Kepler spacecraft for similar and additional science. The K2 mission ran from 2014 until 2018 when Kepler finally ran out of fuel and was retired. As before, K2 monitored stellar brightness to detect transits as well as other uses of such observations. Due to Kepler's reduced number of working reaction wheels (i.e., the failure that retired Kepler's primary mission), K2 made use solar radiation pressure as an element in controlling its direction, with somewhat less precision but sufficient to produce results. It monitored multiple fields for limited periods of time because its movement around the Sun would slowly change the regions of the celestial sphere that it could point at using this substitute method.
Among its projects were surveys for transits across nearby M dwarves (M-type star, red dwarf). This is similar to the TESS mission, but K2's sensitivity and reach were different than TESS's and K2 carried out longer observation periods, since TESS is dedicating its limited time to covering more of the sky.
EPIC stands for Ecliptic Plane Input Catalog, a catalog of stars chosen for K2 observation.