Great Vowel Shift

The Great Vowel Shift (GVS) - named so by Danish linguist Otto Jespersen - was a period of shifts in the pronunciation of vowels the English language. It took place approximately from the 15th century (the late Middle English period) until the 18th century (the Early Modern English period). This is the main reason why English words often sound different from how they are spelled.
Furthermore, coinciding with the development of print, the Great Vowel Shift and the increasing production of printed materials have brought about the standardisation of the English language as we know it today.
Changes
This change was often divided into two phases (with a following third period in Early Modern English with less critical, minor changes) and varied slightly throughout English dialects. It concerned long vowels, short vowels and diphthongs and from the 1400s continued for several centuries. Some consonants' pronunciation changes as well and these changes are sometimes described by scholars when discussing the Great Vowel Shift.
During the period of Middle English, there were five short and seven long vowels. Through the GVS, the long vowels /i:/ and /u:/ gained counterparts they did not have before, restoring the balance in the vowel system. This attempt to achieve balance is thought to be one of the reasons for the start of the GVS. Along with other theories, like the pull-chain and the push-chain theories.
The pull-chain theory suggests that the first to leave their positions were the higher vowels which then pulled the lower vowels to move too. The push-chain theory offers the opposite solution suggesting that the lower vowels were first to move and after they were raised, they pushed the higher vowels up from their previous positions.
The change of pronunciation during the GVS affected long stressed vowels. Therefore, "y" in "only" didn't change pronunciation because it is not stressed. But the same vowel changes pronunciation in the word "my" because it is stressed. The place of pronunciation in the mouth changes, it shifted so that is was pronounced in a higher place in the mouth.
How do we know?
It is important to note that distinguishing the Middle English pronunciation is just an approximation done by scholars because there aren't any recordings of spoken language from that period.
Examples
The following tables show the changes in vowel pronunciation on specific examples.
Historical Division of the GVS
Most generally, the researchers of the GVS have divided it into two phases, which coincidentally correspond with the periods of writings of the two famous English writers: Geoffrey Chaucer and William Shakespeare. Consequently, Chaucer's and Shakespeare's writings are often employed as the most representative examples of the Great Vowel Shift's changes.
Social and Cultural Influences
The exact pinpointing of the period of the Great Vowel Shift and the reason for its occurrence remains unknown to this day. However, there are several theories which are the most frequent, the most widely accepted, and also interconnected through the notions of social emancipation and elitism.
Plague or the Black Death, fast-tracked the levels of migration in England, with the capital and South England as the final destinations. The explanation for this choice of destination of migration might be that despite the infection being present everywhere throughout England, the death rates differed - with the southern part of England as the area with the lowest levels of casualties. The reason behind this is that this area had been majorly inhabited by the royals and the aristocracy, which meant better hygienic conditions and higher levels of health care - essentially presenting better chances to resist, counter and overcome the plague. Furthermore, the surplus of inhabitants in the capital might have fuelled the urge in the original inhabitants to differentiate themselves from and place themselves above the migrants culturally and socially, through a "more advanced" pronunciation of vowels.
The Hundred Years War and due to it, the presence of Frenchmen and with it the influence of French loan words during the Middle English period, which due to thousands of borrowings (mainly vocabulary connected to the government, war, church, law, cuisine, and clothes), transformed the English language, including its pronunciation.
Another factor might have been the middle-class hypercorrection as an effort to imitate the aristocracy's more prestigious French pronunciation, as French was the language of aristocracy, diplomacy, and law, spoken by the ruling class. Inversely, the shift might have also been influenced by the anti-French sentiment in England caused by the wars with France and the people's efforts of distancing themselves from the French way of speaking.
References
English language
Linguistics