I got this item from a quest and its account locked so I would assume it's important. What does it do? I don't want to waste it.

It's dropped by certain challengers actually and it can grant your pet 1-3 health Points if used on them.

permanent buff or just a heal?

Permanent buff. :) It's a stat booster.

the stat boosting eggs only work on pets that are tier 3 or lower, so if you have a pet you're training/battling with, be sure to use the eggs on them before they surpass tier 3 or else they won't be able to benefit from them.

Epic!! Thanks a ton for the explanations! <3