Hello,
Depending on the age of the baby,it can be due to two reasons.If the baby is just born and under two weeks of age,then it can be due to blocked tear ducts.
If the baby is older,then it can be conjunctivitis.Depending on whether it is bacterial or viral conjunctivitis,antibiotics may be needed.Pls consult a pediatrician /eye specialist for that.
Hope it helps.Take care and pls do keep me posted if you have any additional doubts.
How old is your baby? Newborns tend to have clogged tear drainage ducts which can cause a discharge which resembles pus. Try holding a warm wet washcloth over your baby's eyes for a few minutes, then gently wipe the lids and lashes with the cloth. This can help. If s/he seems to be bothered by them, itches at them, or if they are red you might want to visit an eye doctor to see if s/he has an infection.