The Great Vowel Shift was a massive sound change affecting the long vowels of English during the fifteenth to eighteenth centuries. Basically, the long vowels shifted upwards; that is, a vowel that used to be pronounced in one place in the mouth would be pronounced in a different place, higher up in the mouth. The Great Vowel Shift has had long-term implications for, among other things, orthography, the teaching of reading, and the understanding of any English-language text written before or during the Shift.
When we talk about the GVS, we usually talk about it happening in eight steps. It is very important to remember, however, that each step did not happen overnight. At any given time, people of different ages and from different regions would have different pronunciations of the same word. Older, more conservative speakers would retain one pronunciation while younger, more advanced speakers were moving to a new one; some people would be able to pronounce the same word two or more different ways. The same thing happens today, of course: I can pronounce the word "route" to rhyme with "boot" or with "out" and may switch from one pronunciation to another in the midst of a conversation.