Hyzer is the natural fade of the disc, and anhyzer is the opposite. So if you're throwing right hand backhand or left hand forehand, the disc will fade to the left. Throwing it on a hyzer route will let the disc do the work in fading to the left. Throwing it on an anhyzer route means purposely turning the disc over so it fades to the right.
If you are throwing right hand forehand or left hand backhand, the disc will naturally want to fade to the right, so the opposite of above is true.