What does “K2 Twisting” mean? Is it just telling me to twist the stitches before I knit? Yes, this is on a circular needle.
It could be a twisted stitch, where it’s like a little cable. You would knit the second stitch from the tip of the left needle, then the first stitch and then slide them off together–essentially putting the second stitch on your right needle first.
Does the pattern look textured? Just twisting the stitches before you knit them would make it tighter, but wouldn’t show very much.
ok, that makes way more sense than my braindead interpretation. And yes, it is a textured pattern. The pattern is called “Mock Cable Hat” (and I found it online, so if you just search on that, you’ll find it quick I am sure!) I’ll try that and see how that works. 
Now, get this: I just followed that instruction. And I’ll be darned if the finished effect doesn’t look just like what I got when I implemented the instruction (on the first half of the hat) to “Knit first two stitches together, leaving them on the needle, knit again in the first stitch and drop both off the needle.” Maybe it IS slightly different. But any idea why one approach versus the other?? I’m just way too curious. 
I just looked at the pattern, and I see what you mean. The directions are for something very similar–just a different variation, I guess. I think when you do the knitting the two together and then knitting the one stitch, you’re twisting them and also maybe making them a little tighter so they stand out more.