Possession is only explained in Rupturefarms but there is a scrolling display that explains that muds can be freed by leading them to bird portals and chanting.
In-universe, I would say that it's something muds can innately do but Abe only realised at the beginning of the game that it opened portals.
EDIT: I found the screen where the display talks about chanting. I cut and pasted to get the whole text.
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