I'm not sure if there's an explanation for why jazz uses 7th chords so often, it's just what jazz is. Extensive use of 7th chords is one of the main characteristics of jazz harmony. You could play a purely triadic piece in a jazz style but I suspect it would sound a bit childish. The 7th chord tends to be the building block of jazz harmony, whereas the triad is the building block of common-practice classical music. Tensions in jazz are added with 9ths, 11ths, and 13ths, or with chords built in 4ths (often implying m7 or other chords).Originally Posted by dsampson55
Regarding scales, it depends what styles of jazz you're talking about. The melodies of most standards often come from old showtunes, and tend to simply use the major scale or the blues scale, but improvisors often use the dorian and mixolydian modes extensively because they outline the ii7-V7. (If the piece is fairly diatonic, you're essentially in the major key the whole time, just changing your center).
When you want to go a tiny bit further out, a lot of improvisors like to use lydian, or "lydianized" alterations of another scale -- the sharp 4 adds kind of a bright spicy flavor to a line. Also, modes of the melodic minor scale (i.e. play the melodic minor scale starting on a note other than the root) are used to spice up a line without really going too far "out."
These are just some of my go-tos from my education and playing experience, but I'm pretty amateur as a jazz player. I'm sure Chuck will have a lot more to say when he goes into melody.