Out biggest ability is to detect inconsistencies in people behaviour and abstract ideas.
For example, yesterday I was eating with my father (INTj) in a restaurant and he was explaining me the differences between religion and philosophy. He said "philosohpy doesn't give you definitive answers, but more relative ones; it always leaves you with more questions, unlike religion, which pretends to give you etheral truths".
Later we started to discuss about eutanasia:
He: "...it's persistent vegetative state; PVE is brain death and that's death".
Me: "Nope, it is not."
(my dad starts to be angry)
He: "Are you playing dumb right? In medical history no single person has returned from brain death."
Me: "No... we are not discussing the same thing. You have to understand the point of view of those who are against eutanasia. Maybe they are wrong from a philosophical point of view because a person who is in PVE will never recover, but they say they are still alive and that's a fact; unless the organic functions have ceased, you are still alive... You are telling me that once you are in PVE you are dead and that's not true".
He: "Don't start that, can you?"
Me: "But it's true. Rocks are 'dead'. A person is not only the mind, but the whole body, and if it is still alive, well, it's alive."
He: "Hey... but do you think they are really alive? They are usually supported by several machines..."
Me: "So does the people who requieres a dyalisis machine, are they 'dead' too?"
(my father gets even more angry)
He: Aja, and I am using glasses...
Me: "I'm just telling you that they are stating a fact: the body (and the reptilian brain) are still alive and thus, you are still alive..."
Me: "You just said when we were eating that philosophy doesn't give definite answers, so you can't make definite statements about eutanasia".
He: "Oh, well. Shut up."
That's probably why Thomas Huxley could debate with anyone and win. We are masters of empathy and can understand opposite points of view perhaps better than any other type. We might not be as good with logic as other types, but we don't really need it. Instead of thinking by ourselves, we generally just go and happily collect concepts from other people and apply them when necessary. By doing so we save a lot of time about creating ideas and instead spend quite a bit of it thinking how those ideas relate to others. Thus we can beat anyone down given enough "training", even an INTj genius like my dad.
Unlike sensors, whose abilities seem to be mostly innate, we intuitives need to train ourselves in order to be effective. That's why so many ENFp seem dumb and frivolous: that's their "undeveloped state". However, for those lucky ENFp who were raised in a stimulating (intelectual, artistic and such) enviroment, more often than not they are seen by others as extremelly bright and refined. "Perfectly rounded" as someone described Huxley.
Modesty, of course, should be erradicated for our own good