First of all, the key to the "jazziness" of the dominant seventh chord is found in the shell of the chord. A shell is simple (striped down) voicing that uses only the key components of the chord. For a piano player (playing a rootless voicing) this is the 3rd and 7th of the chord. These two intervals alone can define a chord as a dominant seventh.
The interesting part here is that the interval between the 3rd and 7th of a dominant seventh chord is a tritone. A tritone is the exact bisect of an octave, so it is a symmetrical and versatile interval. This quality of the chord allows you to apply the greatest amount of alterations to the upper extensions (in comparison to other seventh chords). Being able to use flat 13ths, flat 9ths, 11ths, natural 13ths and so on; provides a wide color palate for a musician to paint with.
Another interesting resulting from the 3rd and 7th of a dominant seventh chord is tritone substitution. The 3rd and 7th of one dominant seventh chord are the same pitches at the 7th and 3rd of dominant seventh that is a tritone away. Wow, that sentence was confusing. Let me break it down. For example, in a G dominant seventh chord B is the 3rd and F is the 7th. The chord that is a tritone (above or below) G is Db (or C#). In a Db dominant seventh chord F is the 3rd and B (or Cb) is the 7th. The two chord share the same shell pitches. This makes them interchangeable. You can use a Db dominant seventh chord in places that normally call for a G dominant seventh chord. This adds to the versatility and variety of uses available in dominant seventh harmony.