What makes someone "more" or "less" grounded, and how does this make electrocution more dangerous?
electrocution isn't the act of you touching something, but the act of current flowing through your body.

Current flows from somewhere to somewhere.

So, in the examples you bring, current flows from the plug, through your body, to the ground. 

If there's no ground connection, nothing happens (ok, you might feel it shortly when your body gets charged, much like a spark from a rubbing-charged balloon). That's why birds can sit on high-voltage lines without being roasted instantly.

If you're "somewhat grounded", you have a high resistance in the plug->body->ground circuit. (I say circuit, because at the "other end" of the plug, there's a power plant, which also has a (virtual) connection to ground, so the loop's closed.)

High resistance means at the same voltage, less current flows. If you've now got wet hands, the plug->skin->body resistance gets very low. If you're standing in rubber boots, the body->ground resistance gets high, but if you stand on a steel tower with sweaty feet –> baaad news.