The word "draw" has several meanings. Usually it means to make a picture of something. "Can you draw a horse? No, I'm a terrible artist." But "draw" can also mean to "pull something towards you". So if someone says "you can draw water from the well" it means you can lower a bucket into the well and pull up some water. Other examples... "He doesn't race, he's a draw horse." - Means this horse is used to pull a cart. "She'll draw him aside and tell him." - Means she will pull him away from the other people. "Draw a bath." - Means you open the faucet and fill the bathtub with water. "Draw up your knees" - Means you pull your knees up close to your chest.

This would be far easier to describe with a picture. The writer is describing the position in which the character is now sitting, so buttocks on the floor, feet next to buttocks, legs in a position bent in the middle whereby you are able to rest your chin on your knees almost , also you are able to wrap your arms around your legs. draw up your knees = to bring your legs closer to your body