Kids learn to speak by imitating their parents, or anyone else around them. It stands to reason that two kids at the same stage of development would carry on a conversation using the vocal inflections and even accompanying gestures that they've seen many times. They're just practicing their skills.
Once when our son was about that age, my wife asked me a question. My answer was like "Well, we have to wait until we hear back from them, and we still need to find out what size we need." My son looked at her, and in the exact same tone of voice, he said the same thing, in baby babble. The rhythm of his words and tonal emphasis was identical. It cracked me up, and I literally fell over on the couch. My son then came over and went face down on the couch next to me, which made me laugh even harder.
So anyway, possibly mindblowing if you don't have kids. Otherwise, just kinda cute.