Cosmological Red Shift, or Einstein Shift is a phenomenon which we think accounts for the progressive increase in the shifting of spectral lines in more and more distant objects in the universe, as a consequence of the expansion of space.
This is not the same as Doppler Shift, because it is not induced by the motion of an object moving relative an observer. Instead this stretching of the wavelength is due to the fact that in travelling through space, the very space through which the light is moving through, is expanding! Just like if you glue your sock to a rubber strip and then stretch the rubber strip, your sock too will stretch with it! In a similar manner the wavelength of the light is stretched out as the space through which it travels expands.
As for many other phenomena in physics, humans have very little direct experience with the 'stretching of space' but we think that this is what is going on on a vast, 'cosmological' scale.