A catalog number is the identification number a record label assigns to a release. It is used for tracking purposes by both the label and the distributor. Catalog numbers are typically printed on the spine of a CD and on the back of record sleeves, but you sometimes you'll find them in other places on the artwork - and sometimes on the CD and the info label on the record itself.
There aren't any rules as to how a label decides to set its catalog numbers, but once you develop a system, it makes sense to stick with it. Catalog numbers typically include both numbers and letters - often some portion of the record label name combined with numbers that signify the number of the release for that label. For instance, label XYZ might assign their first release the catalog number "XYZ01," their second release "XYZ02" and so on. In this way, you can often trace a label's history by looking at their catalog numbers. Sometimes, labels opt for starting out with higher numbers so they look more experienced - ie, "XYZ125" for their first release - and sometimes labels choose letters that have nothing to do with their label name. Again, their are no rules. As long as the numbers help the label and distributor track releases, anything goes.
When labels release music in different formats, sometimes they manipulate the catalog number in some way so that it also indicates if the release is CD, 7", 12" and so on, but not always. One example of a record label that used catalog numbers in a creative way is Factory Records, who assigned a number to just about everything they did, including gig posters and even a lawsuit (FAC61 is a lawsuit between Factory and Martin Hannett). When Factory Records boss Tony Wilson passed away, his casket was given the number FAC501.