It's all about language acquisition. The concept of pronouns is a little advanced for a 9-month-old who is only vaguely grasping the concept that everything has a name to begin with. When I refer to myself as "Mommy" to my daughter, it reinforces to her 1) who I am and 2) that I have a name just like everything else. While its initial use is for language development and acquisition, it does sort of eventually become a habit--especially if you have children born back-to-back. My son is pretty advanced verbally and, at age 4, certainly has mastered pronouns, but now my daughter is learning to talk so my husband and I never really got out of the habit of referring to ourselves in the third person.
Clearly there are parents out there who don't refer to themselves in the third-person and their child eventually sort out the difference between common nouns and pronouns, so I don't know if there's any evidence to suggest that it advances your baby's language development any faster, but I think many parents do it naturally without even really thinking about it.