The most common "jazz scale" that you will see taught is what is called the "melodic minor scale;" also called "jazz minor", "jazz melodic minor", etc. Simply put, this is minor scale with a major 6th and 7th. There is also the existence of "melodic minor" in classical music, which is that same scale going up, but natural minor coming down. For our purposes, this does not apply but the jazz melodic minor scale is very useful. The sound may be a little strange at first, but once you have an understanding it begins to help all those jazz solos you have been hearing over the years make sense.
Here is a breakdown of the scale as it compares to the regular minor scale;
A - B - C - D - E - F - G
A melodic minor:
A - B - C - D - E - F# - G#
If you are familiar with modes, you also have modes with this scale as well. If I were you, I would start with this scale and get familiar with it's shape and sound. Once you get it under your fingers, than figure out where it applies in jazz. For that, there are certain chords which are ever present in jazz where this scale could be used. Before we get into all that, try and get this under your fingers first and than let's take it from there.
Feel free to correspond with me about this via my "Ask Douglas Showalter" thread, and let's work to help you understand this great concept.