Webbed fingers and toes, otherwise known as "syndactyly" does not have an exact known cause.
Because of certain and somewhat common patterns of its appearance however, scientists have linked it to down syndrome. Another common connection seems to suggest it is a hereditary genetic mutation.
In extreme and rare cases there are a number of genetic "syndromes" that webbed fingers/toes have been linked to. In one, it is related to the mother taking a certain drug during the early stages of pregnancy. For a more complete list of these you can follow the link below.