Given that, the approximated dates for this period is 1600-1750.
The name comes from, oddly enough, a Portuguese word: Barroco, an irregular pearl that is both precious and deformed. The later Rococo (1720-1770 approx), which was very decorated, obviously derives from this too somewhat. Alternatively, the two styles can be amalgamated into one as simply 'Barroco'.
The characteristics of the Baroque can be identified by the use of mirrors, gold, swirls, grandeur, richness, emotional exuberance, movement, tension...you get the point. Mostly though, the Baroque put a great deal of emphasis on the unification of painting, sculpture and architecture.
As is true of every period of artistic movement or style, there is always a historical backdrop. Baroque too was a result of its environment. In the 17th century, all the states we can identify today were more of less established in Europe, except for Germany and Italy. There was also a religious war in the mix, at the hand of Henry VIII's split from the Roman church.
Although we all know Henry VIII turned his back on the Pope because of his wish to divorce, the Protestant force that came to be got their name from the verb 'protest'. Although the king took his stance for less than holy reasons, the people who supported him did so in protest of the Pope's behaviour; (if you've ever watched Da Vinci's Demons, although set a century earlier the Pope Sixtus IV behaviour wasn't massively exaggerated - and we can only assume the likes of Paul III were similar!).
Right so, the aftermath that ensued lead to Europe being split in two: Catholics and Protestants. The Protestants banned idolatric practice. In other words, Protestants did not believe in the use of idols in representing the holy. Thus, art in Protestant countries was far more rigid and scaled down than in the Catholic countries. In the southern Netherlands, being under Catholic Spanish control - see here - all churches were whitewashed and can still be seen today.
The Oude Kerk in Amsterdam, originally covered in frescoes but was white-washed by the Protestant church.
While the arts were being affected in this way on the Protestant side, the Catholics were also appropriating the arts to serve a new purpose...cue the 'art of persuasion'.
Between the years of 1645 and 1663, the council of Trent met 25 times to re-establish the beliefs of the Catholic church. The main principles were that the church had to become clear, persuasive and sublime; and to enforce this, they applied it to the arts. There was also recommendations from the council to portray realistic interpretation of the Gospel and an 'emotional stimulus to piety'. If the Protestant's turning their back on Catholicism was the reformation, then the Catholic church redefining themselves was the counter-reformation.
So why would any of this matter? because it influenced the likes of chuches in Gran Canaria here and art in the Netherlands as pointed out above and seen here/here. It was also very influential on architecture in England, Italy and France.