Your baby's grasp is getting stronger as the days pass by. Babies are born with this grasping instinct. Whenever you will place your finger on your newborn’s palms, she will curl her fingers around yours. This is a more a reflex for newborn babies and will remain the same till your child is about 3 months old. After that grasping will be more a voluntary skill that your child will learn and not just an instinctive action.
Your new born baby is grasping your finger as an instinctive, involuntary action. With time your baby will have more control over the fingers and will start clasping and unclasping the fists. Slowly, you will notice your baby grasp with one hand. She will even try to grab some colorful objects. Eventually, your baby's grasping reflexes will improve with time.