OK - I'm no expert, but still here goes an attempt to explain this. Anyone who knows better - please feel free to correct anything where I might be wrong!:
The GDS availability is kind of like a contract between the airline and the GDS
The letters (like C, J, Z) are the fare code/fare buckets
The numbers following the fare bucket are the number of seats that the GDS can sell at that fare code.
Hence C4 means - the Airline is telling the GDS that the GDS can sell *Atleast* 4 seats in full fare business class. There might in fact be only 1 or 30 seats available in Business class, it's just that the airline is authorizing the GDS to sell up to 4 right now.
The fare code decides the rules (refundable etc.) and the price of the ticket sold
Some airlines offer only 4 seats to the GDS at one time, other airlines 7, and most offer 9 seats
Typically the fare codes are arranged in the descending order on price
Hence if you see the last fare code has 4 (or 7 or 9) seats, that means the airline is still willing to sell lots of cheap seats
If the cheaper fare codes have no availability, but only the full fare has availability (Y, B, H etc.), that probably means the flight is already sold out (or close to it). The airline is now happy to overbook at high fares and if needed they'll bump (up or off) someone in case there aren't too many no-shows.
Airline inventory management systems, might open up a few "cheap" seats on the last day, or if they see a flight filling up fast, might reduce the availability of the cheaper seats. That's all dynamic and stuff that has the potential to change every minute.
IC and AI use their own "private" internal seat inventory system, which has a poor interface with GDS. Hence even though the GDS may show full or no availability, the AI/IC flight might be actually be the opposite. Hence agents have to use a seperate "terminal" when booking IC/AI and that terminal is often "down" or "slow". It's time AI/IC moved to using a standard booking engine/platform.
Jet, Kingfisher, S2 now use the standard GDS platforms, and hence their availability is generally quite accurate. As an example IT has gone with Sabre as their primary GDS system, and Jet probably uses Sabre as well (I'm not sure).
With international carriers, I think a lot of the *A carriers use Amadeus as their preferred GDS system, so I generally rely on the Amadeus system for *A availability
LCCs like DN, 0S, 3K etc. don't upload their inventory to GDS systems at all. They maintain their own systems and need to provide interfaces for 3rd party booking engines (like DN must have provided an interface that indiatimes or travelguru uses to access DN inventory).
GDSs offer much more than just seat inventory/booking. They can basically automate almost all aspects of your airline, including check-in, boarding, baggage tracking etc. Each aspect is charged, and hence airlines need to choose on what they'd like to build vs. what they'd like to buy (from the GDS).
Coming to your specific question:
C/J/Z/I are the Business class fare buckets. One of these code might be an "award" bucket on certain airlines, and an "upgrade" bucket on other airlines.
Y onwards are the economy fare buckets.
The *A Booking classes page on flyertalk gives the detailed explanation for the fare codes/buckets for most *A carriers. It's the same concept for most carriers, except the specific codes are almost always different (except for standards like F, C/J, Y/B/H/M etc.)