'z' is the symbol conventionally used to quantify redshift.

The Universe is Expanding

Because of this, once you are looking 'quite a long way away', everything in all directions is moving away from us. Things further away from us are moving faster away from us. On large scales, this is a sensible way to measure the distance.

The Doppler Effect

When a light source is moving away from us, the Doppler effect reddens the light as we see it. One way of thinking of this is to imagine the light waves being 'stretched' as the retreating object pulls away. Red light (at one end of the visible spectrum) has longer wavelengths than blue light (at the other), and so the 'stretching' effect is described as a reddening.

A Distance Scale

We know the wavelength of spectral features when they are emitted, and so when we observe a distant object, we can measure just how much the wavelengths have been changed.

If the observed wavelength is as much as double what we know it must have been when the light was emitted, this extreme redshift tells us that when the light was emitted, the universe was only half the size it is now. That's a long way away, and a long time ago.

z Defined

A quantifiable measure of redshift is the ratio of the wavelength of received light to the wavelength when it was emitted.

'z' is that number, minus 1.

That way, z = 0 corresponds to no redshift at all, and z = 1 corresponds to a doubling of wavelength.

How Far Can We See?

The most distant objects detected so far are galaxies with redshifts near z = 5 or 6. That's most of the way back to the Big Bang.