Pretty much as the title says. In the Hall of Fame, there's a list of Power Ratings, and my name is moving up and down it. I'd initially assumed it worked its way up as you progressed through the game, but it now seems to be backtracking, so now I'm confused.
I'm not 100% sure on this, but I think power rating is based on the words you create. The better the words, the higher your power rating. It only applies to the adventure mode.
From the FAQ:
If I recall right, it's affected by the length of the word, the letters/tiles used and power-ups/power-downs. Using "gold" letters instead of "copper" will boost the power rating.
The Hall of Fame shows the letter grade version of the power rating that's likely averaged over your play time.