'Cosmological Redshift' (with regard to cosmological luminous objects such as galaxies, quasars etc) refers to the observed lowering of spectral frequencies caused by the high speed motion of astronomical objects away from an observer.
Now routinely measured, it's taken to mean that all objects in the universe are moving away from each other. That's to say the universe is expanding in all directions (currently thought to be due to the effects ofDark Energyplugin-autotooltip__plain plugin-autotooltip_bigDark Energy
"The observational results of the latest 15 to 20 years have established a standard model for the cosmology which has some amazing consequences. A mysterious entity, the dark energy, has been confirmed as the dominant component of the Universe, and is also responsible for its accelerated expansion.).
In the late 1960s and early 1970s, as the list of discovered red-shifted objects grew, it was noticed that the degree of red-shifting sometimes appeared to be 'quantised' (i.e. having 'bunched-up' values rather than a smooth distribution) - with the implication that the velocities at which objects recede tends to be grouped around certain speeds. (example)
Since then, some data compilations appear to confirm that the effect is real - while other surveys imply that there is no such effect.
If the effect is real (and not simply due to errors in measurement) there is currently no explanation for its existence.
If it's not real, there is also no explanation regarding how errors in measurement ('artefacts') consistently appear to show the quantised variations.
Further reading Phys.Part.Nucl.Lett.4:5-10,2007
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