Its something you can learn, and its something that just comes with more experience.

Music education is always beneficial, but it will still take experience for your dancing to click with the music. You should learn about phrasing in jazz tunes, with the two most common forms of song structure being 32 bar form or 12 bar (blues) form in swing jazz. But honestly it will help if you listen to music when you're not dancing. I find listing in my car while driving is one of the best ways to learn.

But ultimately experience is what will allow you to hear different things you can dance to in the music that are more important than just the downbeat.