Baroque was the predominant Italian style of the 17th century. It evolved in Rome between 1620 and 1660 as an expression of Catholic resurgence under the Counter Reformation. (a reason why it was replaced by Classical in Georgian England was that under Protestant kings a Catholic style was decidedly not 'PC'.) Baroque style's main features were lavish, heavy decoration and curvaceous, complex forms.
It was adopted by architects in England during the late 17th and early 18th centuries. St Paul's Cathedral by Sir Christopher Wren is its outstanding example. Wren's example led to an English Baroque school under Wren's assistant Nicholas Hawksmoor (1661-1738) and Hawksmoor's collaborator John Vanbrugh (1664-1726), who designed Blenheim Palace and Castle Howard.
Baroque's main relevance to English house architecture is that it was the style which other styles revolted against. Followers of Classicism and Neo-Classicism came to regard Baroque as a decadent art form which needlessly elaborated designs, and diluted or destroyed simple beauty.