A full Jax skin gallery, plus the practical point: some skins change the silhouette enough to matter in a fight.
Before the cosmetics: Jax is a fighter at 125 attack range whose job is to trade repeatedly, survive the return damage, and win the third exchange rather than the first.

Jax has 20 skins, excluding chromas. The art below is the in-client splash.
Skins change no numbers. They are not therefore free of consequence — a skin that alters the silhouette or recolours an ability changes how quickly an opponent reads what you just cast.
That cuts both ways, and it is the honest reason some players keep the base skin on champions they take seriously.
Jax's consecutive basic attacks continuously increase his Attack Speed.
Jax leaps toward a unit. If they are an enemy, he strikes them with his weapon.
Jax charges his weapon with energy, causing his next attack to deal additional damage.
Jax's combat prowess allows him to dodge all incoming attacks for a short duration and then quickly counterattack, stunning all surrounding enemies.
Every third consecutive attack deals additional Magic Damage. Additionally, Jax can activate this ability to deal damage around himself and strengthen his resolve, increasing his Armor and Magic Resist for a short duration.
Unmatched in both his skill with unique armaments and his biting sarcasm, Jax is the last known weapons master of Icathia. After his homeland was laid low by its own hubris in unleashing the Void, Jax and his kind vowed to protect what little remained. As magic now rises in the world, this slumbering threat stirs once more, and Jax roams Valoran, wielding the last light of Icathia and testing all warriors he meets to see if any are strong enough to stand beside him...
Skins are tied to the account, not to you. Anything bought on a smurf stays on the smurf — worth knowing before spending real money on one.
Full Jax page — abilities, stats and every skin →