Generally used as a compliment to a male. Even more clever, intelligent, good-looking, well dressed, and attractive than just regular sharp, and knows how to manage his facial hair. Used when saying sharp just isn't enough.
A man that is curt sharp attracts every single lady within a four mile radius.
Dude 1: Check out Joe with that well-trimmed-yet-rugged beard! Boy, he looks sharp today!
Dude 2: Nah man, look at the droves of women that are flocking just to get a glimpse of him. Joe is looking curt sharp today!
The only way I can get that bootylicious girl to go out with me is if I am looking curt sharp when I talk to her.