That's always been a tough thing for me to define personally. To me, trying to determine whether you're "really smart" (or not) vs average requires context, I'd need a definition of who I'm comparing to, what subject/fields (or "types" of knowledge), etc.

As others have mentioned, I'm generally good at sensing what I don't know and determining that I need to read up on more about a subject rather than just blindly assuming that I do know it and trying to fix the wiring in my house for example (probably an extreme example, because there's no way I'm ever going to try to do that on my own - even with an infinite time of "research").

I'm a software developer, and my friends claim that this makes me really smart - but when I compare myself to other developers it doesn't feel like that. And yet for being "smart" I am terrible at math.

Maybe its not the simple answer you're looking for, but I guess I feel smart at some things, average in others, and not so smart in certain subjects/fields. I couldn't place myself in a "one-size fits all" answer.