The depletion region is created from the differing majority carrier concentrations on either side of the junction. Holes (h+) move from the P-type side into the N-type side because there are fewer h+ on the N-type side and so statistically, more h+ will cross over than will cross back. For the same reason, electrons (e-) move from the N-type side into the P-type side. This effect is called "diffusion" and the motion of charge carriers arising from diffusion is called "diffusion current".
Diffusion creates a region of "uncovered" negative charge on the P-type side and positive charge on the N-type side. These separated regions of charge produce an electric field (just like any two separated charges of opposite polarity) which influences the motion of mobile charge carriers, pulling h+ back to the P-type side and e- back to the N-type side. This motion is called "drift" and the associated current is called "drift current". In equilibrium, drift and diffusion balance each other out; for every charge carrier that diffuses from one side to the other, another charge carrier will drift back in the opposite direction.
The passage you mention concerns carriers that are generated close to the edge of the depletion region, the area where the electric field causes drift of free charge carriers. If a minority charge carrier is created from random thermal excitation of the crystal lattice and if it can reach the edge of the depletion region before recombining, it will drift across the junction to the other side, adding a second component to drift current. This effect is only applicable to minority carriers (h+ on the N-type side, e- on the P-type side) since the direction of the electric field in the depletion region will push majority carriers back.