As a group, their diets vary greatly, they're omnivorous. Their tooth structure is very generalized and their hands are general purpose. The obvious exception to this is humans, who only have opposable thumbs. A tendency towards upright posture. Fewer teeth than most mammals, which means they have a flatter face.
Primates have good color vision and visual acuity, which means they see very clearly.
Most primates are diurnal, which means that they are active during the day. Primates are very smart.