Not sure I can capture the Baroque in a nutshell, but a very brief introduction.
The key to Baroque music is its contrapuntal nature (counterpoint). Whereas classical, romantic, jazz, rock, pop etc tend (thoungh not always) to have a main "tune" and a harmonic accompianament, in the Baroque there are several "tunes" going on at once that relate to one another, both harmonically and in terms of their structure. This can be as simple as 2 voices in a sort of question/answer sequence, such as in the Bach Invention you are playing, or as complex as a six voice fugue.
Basically, you need to learn to treat the voices independently and to interrelate them to one another. I've heard it described elsewhere here as thinking horizontally as opposed to the verticality of other styles.