According to the New Grove Dictionary of Music - and contrary to the witeup by xunker above - the word baroque is a French word which comes from the Portuguese barroco which means a pearl of an irregular shape. This word was used frequently in texts that dealt with jewelery making.
Although it has been assumed (as xunker notes,) that the first application of the term to the arts was in reference to architecture (by Charles de Brosses), the first recorded usage of the term was actually in reference to music, in 1734, in a letter to a magazine, provoked by the premiere of Jean Philippe Rameau's Hippolyte et Aricie in Paris in 1733. The anonymous author describes the style of the music as 'du Barrocque', and complains that Rameau's opera lacked melodic coherence, was full of dissonance, and changed key and meter constantly. in 1739, J.B. Rousseau has written about Rameau and other composers in a poem, calling them 'distillers of baroque chords'.
Thus, the adjective Baroque was used as a pejorative term, in order to differentiate between music that is sweet and songlike, and the new music that was full of dissonance, and made swift changes between moods (as indeed can be heard in French music of the 17th century.)
In crude terms, the Baroque era refers to the years 1600 - 1750. This is the period which marked the shift from contrapuntal to harmonic composition, along with the rise of the basso continuo and the trend from 'mannerism' to 'emotionalism.' The main musical characteristics of Baroque music are the thoroughbass (basso continuo) as a main thread of composition, together with the rise of tonality (as opposed to the mostly modal character of renaissance music) as it finally came to be in the classical era; highly controlled melodic development and canonized emotional gestures (again in contrast to the 'flights of fancy' of the Renaissance;) the frequent use of dance forms and rhythms in bigger secular works; the prominent use of dissonance for dramatic purposes; and the rise of opera.
The Baroque era also saw the decline of the hegemony of Italian music (and culture in general) over the rest of Europe. In the 17th century, French, German and English music became prominent, as can be seen in the works of Jean-Baptiste Lully, Jean Philippe Rameau, Johann Sebastian Bach, Georg Philipp Telemann, George Frideric Handel and Henry Purcell.