Babies are born with primitive reflexes. That’s because myelin, the insulating layer around the nerves that enables the nervous system to function in a coordinated manner, hasn’t developed yet. You know how baby suddenly startles and throws out their arms as if falling? That’s the Moro reflex. It’s involuntary and is a product of a not yet fully integrated nervous system. These reflexes, while completely normal, can be uncomfortable for the baby; they can even interfere with feedings as spasms in the gut can contribute to fussiness and gas. Swaddling is a word you hear a lot, and for good reason. Swaddling your baby regularly can be an effective way to calm reflexes and to help them feel protected and connected. 

Other (completely normal) reflexes you may notice: 
The fencing reflex. Baby will turn their head to one side, thrusting out the arm on that side while the leg on the same side flexes. (This may look like they can't turn their head back to look at you.)

The grasping reflex. Baby will grasp a finger or object placed into their hand.

The stepping reflex. Baby will make a stepping motion with their feet when you hold them upright under the arms.