To dandle a baby or small child is to bounce him on your lap. You might dandle your little nephew to make him laugh.
When you dandle a baby, you jiggle her in your arms or move her gently up and down on your knees. Your eccentric aunt Iris might dandle her big Maine Coon cat on her lap, or her little toy poodle, but you're most likely to find the verb dandle alongside the word baby. The origin of this sixteenth century word is uncertain, though it may be related to the imitative Old French dandin, "small bell."