Sylas was the first champion I got to work on and as is traditional I brought too much ambition and caused a lot of confusion. Sorry internet u_u
Sylas himself can't absorb magic but he is a mage in that he can use/channel magic. Unfortunately he's been locked into some pretty cruel manacles that just happen to be really good at stopping magic creatures. His restraints are made of a material called Petricite that ancient Demacians invented, basically concrete made from ancient trees that were thought to nullify all magic (if you've seen One Piece they are like the Seastone Handcuffs).
But here's the secret to Sylas' power: he has discovered that Petricite doesn't nullify magic but absorbs it. It drinks in all magic voraciously, causing mages to fall to their knees in pain as their power is drained away, but then stores it like a battery. What's more is he has learned how to release it! He's no trained wizard; he can't shape it into complex spells but instead unleashes all that stored magic that's been drained from his body in chaotic bursts.
TL;DR The petricite manacles absorb all forms of magic with seemingly limitless voracity. Sylas is the only mage who has learned how to release it again!