Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Leap Strike: Leap Strike is a good initiator, chasing mechanism, running away tool, and if you get really lucky you can leapstrik onto an minion over a wall. I generally try not to use it as an initiator unless I need to because it has a long-ish cooldown (compared to his other skills early on) and I then use it to chase. It works excellent with Jax's two other skills to cause some havoc.
Empower: Empower is a wonderful skill to put out some extra damage in teamfights, get a last hit on a minion (can no longer hit several of the lil buggers >_<;), or to harass. In my build I try to get Counter Strike maxed but if they mostly have people who won't be dodging your attacks then it is usually worth it to max Empower first. Always Empower before a Leap Strike for even more extra damage.
Counter Strike: Jax's best skill besides his ultimate. The dodge chance gives you wonderful survivability. The stun has several uses. In a close team fight it can stun all of you enemies giving you and your allies the upper hand. It can be used to out damage another physical DPS in a 1v1. It can be used to stop a fleeing opponent long enough for the last three smacks to kill them. You just have to feel when the stun is needed.
Relentless Assault: This is why Jax is Jax (and now his ultimate is even better :D). This enables Jax to get his attack speed to max really, really fast. Then if max attack speed wasn't enough every third hit (wich occurs almost once every second at max) hits them harder.