For Master Yi:
Goggles from the Inventor
The goggles Master Yi wears are a techmaturgical device that was gifted to the champion by Piltover's
own Heimerdinger, the Revered Inventor. Master Yi first used these
goggles when defending his homeland from Noxus invaders in the time
after the League has just formed and before Ionia had affiliated
itself with the League. The goggles are fitted specifically for Master
Yi; while someone else may wear them, they won't receive anywhere near
the same benefit as he does himself.
The one-of-a-kind goggles, known as the "Seven Lenses of Insight", allow Master Yi to see across a
wider range of the spectrum than normal people see. They also give him
abilities not dissimilar to that of real world binoculars and
telescopes. The goggles are synced to Yi's own magical resonance,
allowing him to adjust settings without the use of his hands. He
simply thinks what he needs, and the goggles act accordingly.
Jax is more of a mystery. He has a number of strange characteristics such as two toes and three fingers. Not to mention the strange way he entered the league:
It is seldom the case where a champion is defined by his actions after
joining the League of Legends rather than before. Such is the case
with Jax, for whom the argument could be made that he is the most
prolific tournament fighter currently at the Institute of War. Before
joining the League, Jax was an unremarkable soldier-for-hire. For
reasons known only to the former leader of the League, High Councilor
Reginald Ashram, Jax was put on the top of the list of candidates to
receive a League Judgment - the interview process that either accepts
or rejects a prospective champion. His Judgment was the quickest in
League history, where the Doors of Acceptance glowed and slowly swung
open as soon as it began. Jax faced no recorded Observation or
Reflection during his Judgment.
Jax proved himself to be an immediate terror in the Fields of Justice.
The self-proclaimed Armsmaster of the League rattled off a streak of
consecutive wins that to this day has not been matched. A number of
summoners in the League grew concerned that the perceived objectivity
of the League of Legends would be questioned by the presence of an
unknown fighter who was unbeatable. For this reason, the new leader of
the League (following Reginald Ashram's disappearance), High Councilor
Heyward Relivash, created special restrictions for Jax to fight under.
This was something the League had never done before, and something
which has never been done since. The burly fighter responded by
imposing his own special conditions; as a means of protest, he
permitted himself to fight using only a brass lamppost. Neither the
League's sanctions nor his own has affected his winning ways. The
League has since rescinded its sanctions, but Jax has not; he fights
and fights well with his trusty brass lamppost.
So I don't believe there is an official reason for him to have a multi-eyed mask on.
Although, I think the real reason is drawing pupils is hard (I swear I've seen someone from Riot make a comment to this effect, but no luck googling it). Notice a number of champions have solid colored glowing eyes.
Backgrounds from League of Legends Wikia