Shakespeare, like any great writer, is a product of his time period. The Elizabethan period was an incredibly rich time full of changes. The English language itself was changing at a rapid pace as new words were added frequently.
When Richard Brubage built the Theatre in Shoreditch, it brought about a great change for theatre companies. They now had a permanent home. Other theatre managers saw the practicality of this and it wasn't long before the south bank of the Thames had several commercial theatre. These theatres needed plays and educated men began to write for the theatre.
Shakespeare himself attended Edward VI school in Stratford-upon-Avon where he received a good education. At that time education was quite rigorous and despite the fact that he did not get a university degree, he was well versed in classical knowledge. His influences include, Ovid, Holingshed, and Plutarch.
The young playwright was also influenced by his contemporary, Christopher Marlowe. It was Marlowe who was the most successful of the University Wits at using blank verse. Along with Thomas Kyd, they used Seneca's closet dramas as a model and they brought violence onto the public stage. Thomas Kyd's Revenge's Tragedy was one of the most popular plays of the period, probably due to the high on stage body count.
Shakespeare was also an amazing observer of the people around him. The result were characters that were believable and real. They were very human struggling with very real problems.
Like all great writers, Shakespeare was influenced by many factors. One was the changing world in which he lived. By this I mean the changing religion through the turbulent years of the Tudors concerning Catholicism and Church of England. Under Elizabeth I, England emerged in 1588 as a major power. He was also influenced by his education and the books that he read and the people he talked to. Finally, using his keen powers of observation, he was able to create memorable plays and characters to populate them.
There was not just one influence on this great writer but many.