All right, I'm not much of an intoduction guy so basically with Jax you want to stay alive until you get your ult. Then get some AS so you can stack your ult and use its third consecutive hit thing more often and deal a ton more damage. THEN you should be fine.

I start out with flat armor marks, then I get dodge chance seals, next I get flat attack speed glyphs and finish up with flat health quintessences. This will make a very beefy Jax and the attack speed with help with his ult(explained earlier).

first aim for ninja tabi for some nice armor, dogde chance, and movement speed(mainly because you want to stay alive until you get your ult). Then grab a hextech revolver and then into a hextech gunblade for some AP, AD, AS, and LS(trust me this helps alot and Jax is very good with AP). Then get quinsoo's rageblade; this will go nicely with your ult stacks. Then I would usually get stinger then into nashor's tooth(AS, AP, and CD reduction... this is a great item for Jax). Then get sheen and turn it into lich bane(so if lich bane passive was used on your ult's passive then you can do massive damage). Finally get malady to finish up Jax. Keep in mind you may build items any way you feel comfortable.

Is there much to explain?

First off I almost always get exhaust 'cause you can catch up to emeny champs or use as a way to escape. Ignite is good for getting first blood and to finish off champs; plus on my masteries you get extra AP when ignite is in cooldown.

Pros

Very beefy
almost unstoppable
great damage output

Cons

somewhat squishy early game
high priced items

Thank you for spending your time looking at this build and if you have a comment/concerns leave a message in the comment box and I'll answer you back as soon as I can:).