I think the term "privilege", outside of academia, may be rather unhelpful on the whole because people will inevitably apply the common parlance meaning to the term. Hence the myriad explanations of how white people can't possibly have "white privilege" if they're also "underprivileged" on the whole.
This approach takes one word and applies multiple meanings to it - no wonder people fail to grasp it!
I personally like to describe "privilege" (in the sense of "white/male/etc. privilege") as "the option of generally not having to think about your skin colour/sex/etc. specifically" and I happen to think it does a better job of making the concept accessible.
Now, as it happens, I'm white. Actually, I'm "white for a white person", complete with light skin and hair and blue eyes. White privilege most certainly applies to me. But also, I don't really understand it on more than a theoretical level.
I do, however, understand male privilege exceedingly well, having graduated in a field that was, at the time, almost exclusively male and having gone on to work in it.
Male privilege is when you're in a conference room with 20 people inside. 19 of them are male. The remaining one is you. None of the 19 even notice and your boss expresses surprise at you even bringing it up afterwards and thinks you may have a bit of a bee in your bonnet. You're actually the second most senior person in the room. You're also the main speaker. You're certainly not "underprivileged" compared to the rest of the room in any general sense. But you very much are different in one particular aspect. And, unlike everyone else present, you don't have the luxury of just not noticing.
Unlike the rest of them, you got up that morning and considered what to wear: trouser suit to look more like everyone else? But physical attractiveness plays a bigger part in your success or failure than it does in theirs? Curve-hugging shift dress, then? But it'll run the risk of them seeing more woman than professional and undermining your standing! Makeup? If so, how much? Does red lipstick stand for "vixen" or for "I have the confidence to pull this off?" Heels, so that you're not by far the shortest? Or flats, in which you'll be more comfortable and it'll show in your posture - but also everyone will, literally, be talking down to you?
Meanwhile, your boss got up that morning and put one any of the suits in his wardrobe. Later, he'll nonchalantly tell you that you, too, should invest in five identical suits and just how practical this is. That's male privilege!
I imagine white privilege must work much the same from the perspective of those who don't have it.
As stated, I'm white. But i believe others when they tell me about their experiences. The not needing to give it any thought part is precisely what privilege consists of. So, no, of course we don't get white privilege. We can try and empathise and make it relatable by comparing to something we do know. Male privilege for me. It may be a bit similar - but never quite the same. That doesn't mean it's not real.
But, again, the terminology is rather unhelpful.