Have you read Pool School? :-D
CYA is Cyanuric Acid or "stabilizer/conditioner". It's like sunscreen for your chlorine.
It is sold separately, but often it is combined with chlorine into trichlor tablets or granular trichlor or Dichlor (often labeled as "shock"). Over a period of time, when a pool is chlorinated thru tablets and powder "shock" bags (Dichlor) the CYA gets too high and "normal" chlorine levels become ineffective. If you look at the CYA chart, you will see the higher the CYA level, the higher the FC must be to keep the water properly sanitized. An overstabilized pool like your's is especially common in warm climates like AZ where pools are open year round and the CYA level is never diluted thru water replacement. In areas of the country where 1/3 of the water is drained out annually for winterization, the fresh water replacement helps keep those pools' CYA levels more manaeable (they still have problems though, trust me!).
Anything over 50 is high, unless you have an SWG then up to 80 is acceptable. Anything over 100 is way too high. Chemical companies also manufacture testing equipment. So when you see a pool store readout that says up to 200 ppm is ok, it's because they also produce the trichlor chemicals that increase CYA levels to begin with. They don't want to put out anything on a testing printout that may hurt their chem sales.
The only practical way to deal with CYA as high as yours is to do a series of partial drains and refills, to get it down to 60-70 at the very least.
In a properly maintained pool, you won't need clarifier, algaecide, phosphate removers or anything else the pool store will try to sell you. The only thing I've added to my pool in 3 summers of BBB is bleach (and a little CYA this spring).
