Wood stabilization typically refers to reinforcing wood against inherent defects or weaknesses.
In turning, stabilization may mean anything from filling cracks with epoxy, to impregnating the wood with resin.
More generally, you can stabilize a crack with a butterfly inlay or you can again use epoxy or some other filler.
In the case of turning, the purpose of stabilizing the wood is to strengthen it against cracking and shattering while working on the piece. In other cases, you may want to showcase a crack (or other "defect")
as part of your piece's character, but you want to prevent the crack from spreading further, possibly to the point of causing the piece to break or fail. For example, butterfly/bowtie inlays are commonly used to stabilize cracks in large wooden tabletops.