In 5e D&D, the spell Enhance Ability provides a buff: one of six ability scores gains advantage on ability's checks. Perk also happen: buffed-Con grants hit points, buffed-Strength grants double carrying capacity.
Previous versions of this spell directly increased ability scores. This meant characters would become near-godlike, so this confounded game balance. 5e mostly solved this problem. That said, it is unclear how a person performs 'at advantage'. How does it look to others?
Let us take a buffed intelligence score using this spell:
Fox's Cunning: The target has advantage on Intelligence checks.
Imagine an ogre and an illithid (or 'mind flayer') are having a conversation. Both gain the Fox's Cunning transmutation-effect via spell, scroll, potion or what-have-you. They are both somewhat 'smarter' - but how much? How does this present, how does this work and how does this play out in a role-playing situation? Let us examine further.
All mind flayers gain +7 or more on their intelligence rolls. This gain of advantage means almost nothing to such a creature: They go from being amazingly brilliant to being, well, amazingly brilliant. Possibly no real noticeable change at all - not even to the Mind Flayer.
Now let us look at this poor ogre:
Having a -3 intelligence modifier thanks to their 5 base-int ability really hurts. One would assume that even daily basic life skills are a genuine challenge for this creature. That said, this intelligence double-check applies on ALL tasks performed - with a re-try every six seconds. Suddenly life is stunningly easy. Even nigh-impossible things ('nat 20 only') happen 9.75% ('2 x 5% = 9.75%') and every six seconds at that.
How does this role-play itself out? Wild ideas abound. Should a DM just go with some statistical variance and figure out what those rolls kind of resemble or match as an equivalent of? Would this 'super-shmaht yet kinda shtupid wiseguy' just think about it again and now gets it the second time through? Possibly like a stutter that keeps getting smarter with each guess. You might suggest he or she presents as... a bit slow... but sorta... deep... and thorough... somehow? Others might feel this ogre is obviously cheating - it is as if someone, somehow, somewhere is whispering all the correct answers directly into his mind! Now he can even answer totally impossible questions with weird yet astounding accuracy - almost double that of the average person.
Question repeated: In any given role-playing situation, how does intelligence-at-advantage present &/or function in-game?