The Great Vowel Shift is what divides Middle English (the language of Chaucer) from Modern English, the earliest monuments of which include Shakespeare and the King James Bible.
It is possible to understand Shakespeare spoken as he himself would have spoken it: it is done in some performances. It sounds strange, like some unfamiliar rural dialect, but it can be followed. It is impossible to understand spoken Chaucer without some special study.
When you study European languages you find the vowels are usually similar: the letter a is "ah" in German, French, Italian, Spanish, Czech, Polish, etc etc. But in English it's "ay" in gate. The letter i is "ee" as in machine in all them, not our usual "eye". And so on with all the other long vowels: the English is often nothing like the continental.
The gulf between Chaucer and Shakespeare, and the gulf between English and European vowel spelling, is because of the great shift that happened in the fifteenth and sixteenth centuries, and which affected the entire system of English vowels.
It only changed the long vowels. This is why bit and bite have such very different sounds, as do mat and mate. The now-silent -e used to be a separate syllable, and the first one was an open syllable, and pronounced long: bî-te, mâ-te. These long vowels î, â shifted while the short ones stayed much the same. The short vowels (except u in cut, which did its own little shift later) are still quite like the European values they used to have.
There were seven long vowels in Middle English. Because the English spellings are misleading because of the shift, here are examples of the seven vowels using French words as well as modern English ones that are roughly the same:
si fou see food
née eau may owe
mère fort there for
la far
Now here are examples of Middle English words with these sounds:
mine mouse
meet moot
meat moat
mate
So mine had the ee vowel of si, see;
while meet had the ay vowel of née, may;
meat had the air vowel of mère, there;
mate had the ah vowel of la, far;
moat had the aw vowel of fort, for;
moot had the oh vowel of eau, owe;
and mouse had the oo vowel of fou, food.
Then they all shifted up one. Well, the back vowels shifted up one: moat went from "mawt" to "moht", and moot went up to, um, "muut" with the modern "oo" vowel. The front vowels shifted up two: mate went from "maht" up to "mayt" (which used to be spelt meet, there's a quiz on this after), and meat ("mairt") went up to "miit" as in "machine", catching up with meet ("mayt"), which only had one step up to get to the top.
But the vowels already at the highest point in the mouth, the long î, û vowels (û was written ou under French influence) couldn't go higher, so they broke into diphthongs. The front half dropped right down to an "ah" sound, creating "ah-i, ah-u" diphthongs. In other European languages these sounds are usually written ai, au, but in English they're i, ou, as in mice, mouse.
It's hard to be precise about when the Great Vowel Shift began and ended, and in what period it affected this or that vowel or applied in this or that regional dialect in England. In Shakespearean times (c. 1600) the dropping of the diphthongs was not complete.
These changes of all the vowels were almost certainly not independent isolated changes, but happened as a single big rearrangement of the whole system. It could have been either a push-chain or a drag-chain process. A push-chain process would be one in which a began to rise, encroaching on ea, which then began to rise in response, to prevent mate becoming identical with meat.
Alternatively, a drag-chain explanation is that the highest vowels i, u first broke into diphthongs, meaning there were no longer any vowels at the highest position. Then the next-highest vowels, ee, oo, began to rise to fill the gap, then the ones below them also began to rise. I think in this case a drag-chain is more likely. If it had begun with a rising it would only have pushed one column above it.
Why?
Added later. Several people have asked me why this happened. The simplest answer is that we don't know. All languages change all the time, and always have, but there is no general explanation of why one
sound changes into another at a given time in a given language.
Sometimes explanations for individual effects can be given. Sometimes it's influence by a neighbouring dialect or language. Often it's a matter of the new sound or cluster being easier to pronounce. So the ty sound at the beginning of tune has for some become either t or ch, depending on their dialect.
But as both the from and to sounds in the Great Vowel Shift are all normal, common vowels, ease of pronunciation doesn't seem to be it. I don't know if there was any influence from outside at that time. To me, it's just a change, and languages change.
The large extent of the Shift is a different matter. Once the Shift had begun, the chaining mechanisms (whichever one occurred) might have kept going in order to keep words separate. But if this is true, it only applied for a certain time. After all, meat and meet are now pronounced the same, so there wasn't enough selective pressure to force them to remain separate.