What is also interesting is that certain words share similar literal constructions in unrelated languages.
The best example I've always thought of is the verb "to understand". Picture standing under something; you get to know it better.
In my native language Twi [1], the to understand is literally constructed as "to to sit under" I know of several other languages with very similar constructions.
Easy for an adult, not so easy for a baby. Bilabial and coronal sounds don't take much tongue dexterity: you just need to be able to open/close your lips and leave your tongue in its natural resting position respectively to produce them. Velar sounds, on the other hand, require you to flex the middle of your tongue to touch your palate, which is as significantly more difficult sound to produce.
It's no coincidence that sounds like 'gaga' and 'kaka' tend to be associated with either more distant relatives or with defecation: the kid's going to be older when those things get introduced.
There's nothing even slightly strange about it. The terms are self-recapitulating because parents mistake children's babbling for first words. If anything, it'd be strange if they weren't the same. Take a read of this: http://languagehat.com/trask-on-mama-and-papa/
Addendum: in case anybody's wondering what I meant when I wrote "it'd be strange if they weren't the same", I was referring to the high probability of them being coincidentally the same or at least very similar.
And correct, as it happens. Though long-running cultural associations with certain consonants (such as 'm', 'n' and 'b' and mother or grandmother, 'p' and 'd' with father or grandfather, &c.) to play a huge role in it too: the parents need to be culturally primed to mistake the babbling for actual half-formed words, and subsequently build that association in the child's mind in return.
I'm not sure why I was downvoted - Larry Trask's article has the exact same explanation i gave above - mainly that the 'm' and 'p' sounds are the easiest consonant vocalizations that babies can do.