What is meant by 'shifted to the red end of the spectrum' is this:

If you vaporise an element in the lab and pass an electric current through it, you get a glow, the colour of which depends on which element you use. For example, sodium (in street lamps) gives an orange glow, neon (in advertising signs) gives red. The colours emitted by each element have very particular wavelengths that we can measure in a spectrometer, and detecting a particular cocktail of colours in an unknown source enables us to identify which element must have emitted them. A spectrometer separates all the colours out and displays them side by side (rather like chromatography separating out chemicals from a mixture). The order of the colours is red, orange, yellow, green, blue, indigo and violet, so there is a red end of the spectrum and a violet end.

Now imagine that you hear a song played on a cassette. You can recognise it by the combinations of sounds present. If someone slows the tape down, everything gets slower and lower in pitch, but you can still recognise the song - but you'd know that the battery was running down or someone had his finger on the tape. Similarly, when we look at the light from distant galaxies we can tell that it's coming from hydrogen by the pattern of frequencies, but they are all wrong by being lower than they should be - 'redder' in light-speak. And the further away a galaxy is the lower - redder - the frequencies seem to be.