Thomas Wyatt early in the 16th century.Wyatt had brought to attention the beauty and artfulness of the Petrarchan sonnet. Shakespeare made significant changes to the Italian model and introduced his own style, now known as the English (or Shakespearean) sonnet.

The Elizabethan Age is considered the Golden Age of English literature. English writers were intrigued and heavily influenced by Italian Renaissance writing and readily adopted this model. This period also saw the introduction of a new genre in English theatre, the tragicomedy, which became very popular. The era is also considered the era of sonnets. The works of writers such as Shakespeare, Wyatt and Thomas Campion became very popular as printed literature and was widely distributed in households. Drama, under Elizabeth's reign, became a unifying influence, drawing people of different social classes together, since watching a play became a common  experience and was not exclusively restricted to the gentry or upper class. Commoners and royalty could enjoy the same performance in each other's company, albeit in separate seating arrangements. 

Elizabethan Literature has so deeply stamped its authority on all future literate endeavors and developments, that we, almost half a millennium later, still study it and admire its exceptional beauty and greatness.  

The number of literary characteristics of the Elizabethan Age are so numerous one answer can't begin to fully cover the question, but I can get you started.  The Elizabethan Age is part of the English Renaissance.  As such, ideas, forms, themes, etc., from the Italian Renaissance and ancient Greece and Rome lead to what becomes Elizabethan literature.  Poetry, for instance, comes to be dominated by the sonnet.  Poetry moves away from the narrative to the lyric, specifically the lyrical sonnet.  Drama imitates and builds on Greek and Roman tragedy, particularly in the person of Shakespeare. 

Whether you're dealing with poetry or drama, one characteristic of Elizabethan literature is that it is highly stylized, though not as much so as some of the poets that would write later.  Iambic pentameter dominates poetry and Shakespeare's drama.

It is important to remember that the Elizabethan Age existed in the larger context of the European Renaissance. This was a time when new artistic ideas flourished by drawing on various older influences. For instance, the writings of the ancient Greeks and Romans had just come back into vogue. The writings of Plautus, Menander, and Terence had a huge impact on English comedy in the sixteenth century. Seneca and Pacuvius had a similar influence on Elizabethan tragedy. Many English writers were eager to use these Classical sources as inspirations for their own writings. Furthermore, Elizabethan poetry is full of allusions to classical mythology.

Literature of this time also started to incorporate more three-dimensional characters than it had previously. Many of the classical philosophies and earlier Renaissance writings that English writers studied dealt with exploring elements of the human condition. Known as humanism, this way of thinking involves exploring what makes individuals who they are and often delves into their emotional states. This was a stark departure from earlier medieval literature which usually had rather flat characters.

Increased cultural connections with Italy also influenced Elizabethan literature. The lexicographer and linguist John Florio, the son of an Italian, is credited with expanding the scope of English literature by introducing Italian elements. He certainly had an influence on Ben Jonson and William Shakespeare. In poetry, the sonnet can be traced directly back to Italy by way of Henry Howard.