The history of the English language really started with the arrival of three Germanic tribes who invaded Britain during the 5th century AD. These tribes, the Angles, the Saxons and the Jutes, crossed the North Sea from what today is Denmark and northern Germany. At that time the inhabitants of Britain spoke a Celtic language. But most of the Celtic speakers were pushed west and north by the invaders - mainly into what is now Wales, Scotland and Ireland. The Angles came from Englaland and their language was called Englisc - from which the words England and English are derived.
(Read more from http://www.englishclub.com/english-language-history.htm)
So, the English language composes of three phases, Old English, Middle English, and Modern English. Shakespeare wrote in Modern English, but his form of English or called Elizabethan English or Early Modern English. Right now, we all use Late Modern English, which has a lot more vocabulary than Shakespeare's language at that time. Late Modern English has many more words because its Industrial Revolution and techonology led to a need for new words, and also because it adopted more foreign words from other countries.
I think Shakespeare was a really great writer as he created many good writings with as much vocabulary available at that time as possible. He really made good use of the language, and this is why he is as relevant today as he was in his own time, but his language really has quite a number of differences with our current one, which makes reading his works difficult (Especially when I am reading The Merchant of Venice). An example would be the comparative adjective "more" and the superlative adjective "most" being used as intensifiers, as "very" would be used now. I believe Shakespeare's works will still be used for educational purpose in the future as well, as it can show us the previous type of language that was being used.