From my own answer of similar question:

In Despicable Me 2, It is shown that minions have bad eye-sight. Without glasses, minion's vision is blurry. When because of, a purple minion, one of the minions lost his goggles, he was not able to see properly. So that appear to be reason behind wearing goggle.

From my own answer to similar question on sister site:

In Despicable Me 2, It is shown that minions have bad eye-sight. Without glasses, minion's vision is blurry. When because of, a purple minion, one of the minions lost his goggles, he was not able to see properly. So that appear to be reason behind wearing goggle.