Since the action is lower, you don't need to lift your fingers off the fretboard as high as on a high action fretboard. This means less movement. If you have less movement then you can play faster.

Everytime I heard someone someone says a guitar had a fast neck the guitar had a very low action and low frets. Low frets makes it easier to slides so you can go around the fretboard faster with less restrictions. In other words, your fingers don't bump as much on the frets.

But it's not like it automatically makes you play faster, nothing in this world will make you play faster without putting in hours and hours of practice. Don't go and buy a new guitar just because you wanna play faster, that won't happen. Some guitars will "help" you play faster if you already know and apply correctly the different guitar techniques, it won't "make" you play faster.

Hope that clarifies things a little more.