The Baroque period started approximately at the 1600s. Of course, there's neither a way to know the exact date, nor it exists. Because musical periods didn't change like a clock that goes from 11.59 to 12.00, but rather flowed one into the another, and they weren't even conceived as specific periods until many years had passed and they could name them and separate them, for the shake of historic study. But it has to be understood, that periods are just different perceptions of music, that mingle into each other, and what really separates them is the perception towards music itself.
Baroque Music was of course a more general movement of art, and as always, music was the last one to "catch wind". Baroque means more or less "rough pearl", and it's referring to the unwashed beauty that lied behind that art, which was certainly mortal, and therefore not beautiful and perfect, according to the point of view of that time.
The most prominent of the baroque composers was, as I'm sure you know, Johann Sebastian Bach. Other famous composers of that time were George Friedrich Handel, Claudio Monteverdi, Johann Pachelbel, Antonio Vivaldi, Tomasso Albinoni, and others.
Although music in that time was very developed in harmonic progression, harmony in music was not used much out of context. Harmony still existed as a conclusion through counterpoint, as a mean of a counterpoint pleasant to the ear. Baroque composers tried a lot to find new methods to develop harmony even more, because they weren't as much interested in the development of form, which we 're going to see in classical music. We have to admit though, that even if these composers didn't give as much attention to harmony as to counterpoint, that they evolved harmony a lot, since renaissance, and tat harmonic progression was starting to be really present in music.
The end of this period is linked to Johann Sebastian Bach's death, in 1785. Of course, as we said, the periods mingle together, and long before Bach's death, there were many composers that looked at music differently, and were preparing the world for a new age of music. However, there are numerous composers, that are being played until the present day with the same passion as three hundred years ago. That kind of power in some people's music is found in every musical age of the world, and every time differently expressed.
Perhaps the most important factor as to how to determine the quality of the music of one composer, is time. When you look at a piece of music that has been around for four hundred years, you know his composer is good! But that means that people decide what music is worth listening to, and what not. That is certainly the most important thing, and not highly literate music, which is quite clearly for the few who can understand it, and maybe not even them.
Finally, you can be sure, that whatever music from Baroque is kept alive until today, is certainly worth listening to. Twelve generations can't be wrong!