Common causes of constipation are

1. Formula-feed babies (which is harder to digest than breast milk). When using the formula, always use the amount of powder recommended on the packaging. Using too much powder can make your baby constipated and may cause dehydration.
Dehydration
lack of fluids.
Lack of fiber
such as fruit, vegetables, and cereals) in their diet.

 Tips to relieve constipation at home:

1. Gently move their legs like they are riding a bicycle – this can help get things moving.
2. gentle tummy massage
3. In bottle-feed babies try to give some extra water in between feeds only, If your baby's age is more than 6 months.
4. Fibre-containing diet - apples, pears, and prunes are particularly good for constipation.

In spite of all these if constipation is not relieved then organic causes need to be evaluated, please visit the Doctor. 

If untreated it may lead to

Hemorrhoids
Fissures
Rectal ulcers
Urinary retention
Bowel obstructions
Fecal impactions
Megacolon
Volvulus
Fissure in ano