My baby is 3 months old and likes to babble a lot - when I speak to her she seems to be having her a conversation with me. Are we actually talking? Does she understand anything I am saying?

That's adorable! I don't think she understands word for word what you're saying but she's definitely grasping the concept of communicating and bonding with her mommy. Hearing mommy's voice soothes her and she's probably entertained by the interaction :) She's also stimulated by your company and her babbling is her way of responding and acknowledging your presence.