So, yes. This is, essentially, a stylized marabou stork carrying a slightly-anthropomorphized mandrake root in a ruff/pouch around its neck.
As usual, your next question (assuming the above statement answered your first) is probably, “okay, but why?”
I would like to blame the flavor text/Pokedex entries from … gen 1 on, really, though X/Y definitely played a part in this particular fiasco. Various wacky excesses were leading us to ponder the liberal use of overstatement and drama in the descriptive text, perhaps in the hopes of of impressing young children for whom such description techniques are standard. I suggested that some of the more perplexing design mash-ups might similarly represent childhood confusions about plants, animals, objects, etc.; and thus the stork idea was born.
I suppose Howl’s Moving Castle is also to blame at this point, since I recently re-read it against my will (as it turns out, you can not look up just one paragraph or page from that book without continuing on with the rest of it, whether it’s midnight or not), so John Donne’s prophetic poem was fresh in my mind as well. Thus we wound up with the stork’s white ruff and rather unattractive throat-pouch-thing morphing into a removable knotted bag/sling/nest dealio that additionally stands in for the fabled baby-bringer’s most prominent prop, while the baby is replaced by the aforementioned mandrake root. There’s … not much more to be said than that. Aside from the fact that yes, this is drawn on scratch paper and the printed square on the other side is showing through rather aggressively.