Adhere being to stick to the surface of something (ad- meaning toward), and cohere being to stick together (co- meaning with) -- this uses in- meaning, well, in. The Latin stem of all these, for what it's worth, is haerēre, to stick. As for the word, given that the physical aspects of this are hard to imagine, its main use is in philosophy, especially classical philosophy, where the question of what qualities are inherent to things was a subject of discussion. Not that it isn't still, but the question of how we know things at all is now more important.
Within the suit of armor was some dust, a dead silverfish, and a Spongbob sticker inhered within the chestplate.