What does it mean when an infant constantly rubs their eyes and ears?

Many things: Constant eye rubbing can mean many things from simple eye allergies to the infant rubbing eyes because they hurt the infant or has poor vision (oculodugital syndrome). See a your pediatrician first, ask to be sent to a pediatric ophthalmologist. Ear rubbing has not been found to predict ear infections (pediatrics 4.2010) the child is self simulating maybe normal, but good idea to get examined.

Infant rubbing: Eye and ear rubbing by an infant could be habitual in nature but it could be related to allergy, viruses, or other causes. I would recommend ruling out other issues by seeing your pediatrician.