Those are terms used to discribe the flight of a disc. For a right handed-back hand throw, hyzer would describe a disc flying to the left, while anhyzer would describe a disc flying to the right. Reverse this for left hand back hand and right hand fore hand (side arm).
Hyzer and anhyzer are what you do when you release a disc. A disc that is released / (a little less angle.) is a Hyzer and the anhyzer \ (again less angle.) The release is with a right hand back hand throw. The anhyzer is a release I use for an overstable disc when I need it to hold a straighter line longer before it fades. A hyzer is when you would need to make a long right to left shot around an tree or other Obstacle. Hope this helps.
Hyzer is the natural tendency for the disc to turn counter to its rotation. Anhyzer is just making the disc turn the same direction as the rotation by increasing the torque of the throw or through angle of release.
You will also come across the terms "over stable" and "under stable". Over stable discs will tend to "hyzer" hard naturally (drivers) while under stable discs will hold their line or "anhyzer" (think putters).
If you are just starting out you should stay away from discs that are too over stable and stick with something in the Roc to sidewinder range until you can develop some "snap".
I highly recommend the disc golf review forums for some great tips on disc techniques.
Hope this helps and welcome to disc golf. You can check out anytime you like, but you can never leave.
Thanks for all the input.It is winter right now so the course is covered in snow, make it difficult to go out on the course to try some of these. As soon as the weather clears up I will be out there practicing. Of course there are the Winter Warriors who brave to cold and still play.