K2 is the name of a mission reusing what is left of the Kepler spacecraft for the same and additional science. As before, it monitors stellar brightness to detect transits as well as other uses of such observations. Due to the failure of gyroscopes, it is to make use solar radiation pressure as an element in controlling its direction, with somewhat less precision but sufficient to produce results. It is monitoring multiple fields for limited periods of time because its orbit changes the regions of the celestial sphere that it can point at using this substitute method.
Among its projects are surveys for transits across nearby M dwarves (M-type star, red dwarf), complimenting TESS because K2's sensitivity and reach are different than TESS's and longer observation periods are planned.
EPIC stands for Ecliptic Plane Input Catalog, a catalog of stars observed.