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A K correction provides a means of correcting the magnitude of a distant (extragalactic) object to adjust for its redshift, i.e., to give the magnitude it would have if it had no radial velocity, e.g., due to expanding space.
Such a correction depends upon the spectral band as set by the sensitivity function of the sensing instrument and that of any filter: the redshift reduces the photon energy and shifts the band to a portion of the SED (typically) nearer to or further from its peak. A K correction encapsulates this as a quantity, which can be used as a term in a calculation of absolute magnitude from apparent magnitude. Derivation of the K correction for a particular passband and object type is presumably quite complicated, but useful easy-to-calculate polynomial-approximation formulas have been devised from observation data and theory.