Vowel sounds are primarily determined by the position in the mouth where they're voiced, so they're defined in terms of height (or sometimes openness) and frontness or backness. A high vowel is produced near the roof of the mouth, while a low vowel is produced lower, with the mouth wider open.
Vowel shifts are a fairly common thing. Because vowels are not tied to a particular place of articulation like consonants are, they tend to slide around a lot. That is, consonants by definition are produced with restriction of air flow, while vowels are produced without restriction of air flow.
There have been other vowel shifts in the history of the English language, and there are some going on today, but the Great Vowel Shift was by far the largest. The Great Vowel Shift only affected long vowels; the long-short vowel distinction isn't what they teach you in elementary, but rather a literal difference in the duration of a vowel.
This nifty site lets you see and hear each vowel change in sequence. The first step was the diphthongization of the high vowels, /i/ and /u/ (as in modern-day
beet and
boot). Next, the mid-high vowels, /e/ and /o/ (roughly like modern-day
bate and
boat) rose to take their spots. Then /a/ (which doesn't exist in many dialects of modern-day English, but is halfway between the sounds in
bat and
bot) moved forward and merged with /æ/ (as in
bat).
Then the mid-low vowels, /?/ and /?/ (
bet and
bought [for people who don't rhyme
bought and
bot]) moved up and diphthongized at the same time, becoming /ei/ and /ou/. Then /æ/ moved up to take the place of /?/. The new /ei/ then moved again and merged with /i/, and the new /?/ moved up to take the place of /ei/. (That's sort of a confusing sequence; basically, /?/ and /ei/ shifted up twice.)* Meanwhile, the diphthongized high vowels from the first step continued to fall, leaving them with low starting elements.
And that, essentially, is why English vowel characters don't match up with other European languages—our vowels have moved one or two positions (or even three), but we never changed our spelling to reflect the new positions.
*I believe that not all words with these sounds moved twice. That's why we have so many pronunciations of the combination
ea. In Middle and Early Modern English, it was used to repesent the sound /?/, both long and short (the short vowel hasn't changed, so you can still see it in words like
dead and
leapt). However, some of those long
ea words moved up to /ei/ and then /i/ (
neat and
speak for example), while some just moved up to /ei/ and stopped (like
steak).
