Capturing skill gives you a certain chance to "capture" the monsters you kill.
When you succesfully capture a monster, you will receive a doll of that monster, and gain some Capture skill experience.
The stronger the monsters you capture, the more experience you get!
Dolls are used for resurrecting summons, and also to spawn monsters in the town Hunting Grounds. For example, with 50 Man Cow dolls the Head of the Hunting Grounds can spawn 500 Man Cows.
If you want to be a capturer, you'll have to start by reading all 30 books! Then you start by capturing weak mobs first, and you work your way up. Capturing is a Very Time Consuming skill, and it can get very boring.