What does the increase in red shift tell us about the universe?

The next time you're at a railroad crossing and a passing train blows its horn, listen to it. Note that the horn is high-pitched as the train is approaching you, then drops to a lower pitch as it passes by and starts moving away from you. This is called the Doppler Effect, and is caused by the wavelength of the sound being compressed as the train approaches and stretched out as the train recedes.

Red Shift (and Blue Shift) is the electromagnetic equivalent of that. Yellowish light from a source that's rapidly approaching will have a shorter wavelength than if it was stationary, and will appear blueish; if the source is rapidly receding, the light will have a longer wavelength and will take on a red hue.

More generally, anything that adds energy to light will increase its frequency, shorten its wavelength, and "Blue Shift" it; and anything that removes energy from light reduces its frequency, extends its wavelength, and "Red Shifts" it. Relative motion is one way to do this; gravity is another.

A note for the Relativity fans out there: while the speed of light is invariant, its frequency is not. And things that you would expect to increase or decrease speed instead Blue Shift or Red Shift light.