To understand the baroque style, one must understand the impact of the Protestant Reformation on the position of the Catholic Church during the 16th and 17th centuries in Europe. The thinkers of the Reformation encouraged a sparse and severe style, and in response to this, the Catholic Church encouraged the opposite: an ornate, sumptuous, highly decorative style, also known as the baroque. This style impacted the arts in general, so baroque elements can be observed in architecture and painting as well as in literature of this time period.

Contemporary writers of the baroque style are known collectively as contributors to a Neo-Baroque body of literature. These writers are sometimes known for their emotional excess and their embrace of other kinds of excesses, like allusions and certain rhetorical styles. British writer T.S. Eliot, American writer Djuna Barnes, and Chilean writer Jose Donoso have all been identified by scholar Monika Kaup as Neo-Baroque in their style and subject matter.

While we usually associate the word baroque with the visual arts, that association can be helpful in understanding the baroque in literature. We generally associate the baroque period with the seventeenth century, but not all literature produced during that time period was baroque (the seventeenth century also saw the rise of "plain" writing in English literature).

The baroque is the lush, the lavish, the ornate, the dramatic, the curving and twisting (think of Bernini's twisted pillars in the Vatican), the sophisticated and self-conscious, a kind of art or literature that produces a sumptuous feast for the eyes or the imagination. 

In English literature, the metaphysical poets, such as John Donne, pop to mind with their complicated metaphors, but chief exemplar of the seventeenth-century English baroque in literature is Milton, whose epic poem Paradise Lost is lush with imagery and classical allusions, a dense, ornate, erudite masterwork. An example of Milton's lush, dramatic language in that work follows: 

Into this wild Abyss/ The womb of Nature, and perhaps her grave--/ Of neither sea, nor shore, nor air, nor fire,/ But all these in their pregnant causes mixed/ Confusedly, and which thus must ever fight,/ Unless the Almighty Maker them ordain/ His dark materials to create more worlds,--/ Into this wild Abyss the wary Fiend/ Stood on the brink of Hell and looked a while,/ Pondering his voyage; for no narrow frith/ He had to cross. 

Literature of the baroque period is full of metaphor, emblem or symbols, and hyperbole. The purpose of baroque period literature was to move the reader into an emotional state, to lift the reader out of the mundane.

Baroque literature was very complex very much like baroque art and architecture. This very same period in English literature is known as the metaphysical period which focused on the  "unnatural" or "adverse to nature" rather than supernatural. Either way, the baroque period in literature lasts from the end of the Renaissance to the beginning of the neoclassical period when reason and logical senses became the norm.

The Baroque style used exaggerated motion and clear, easily interpreted detail to produce drama, tension, exuberance, and grandeur in sculpture, painting, literature, and music. http://encyclopedia.stateuniversity.com/pages/2383/Baroque-literature.html#ixzz0GztcypUi&A

Some baroque writers include: William Shakespeare, John Donne, Sir Francis Bacon, Sir Walter Raleigh, Capt. John Smith, Theodore Agrippa d'Aubigne, Cervantes (Don Quixote).

The Roman Catholic Church encouraged the Baroque style of art, architecture and literature as a way to influence persons heavenward through the overly ornate architectural styles and art used in the church. This came about after the Council of Trent commissioned art that would appeal to the illiterate masses.

In modern use, the term baroque has little to do with the original time period. Rather, it means any art that is extremely elaborate, overly ornate or overly complicated.