Catalogs are files which contain information about what files have been backed up. Catalogs are used when you create a selection list for a restore, so BE knows what files you can restore, when they were backed up, and what media they are on.
When you run a backup, BE creates a catalog of which files were backed up, and puts a copy in its Catalogs folder, and a copy on the storage media. The copy in the catalogs folder is used when you create the restore for the selection list. The copy on the media is read and imported into the Catalogs folder when BE doesn't have a local copy.
Catalogs can grow to large sizes if you retain lots of data. You can edit the settings in Tools, Options, Catalogs to change how long the data are retained. Full catalogs contain all the information listed above. After a set time, the catalog can be truncated, so that the file and directory information is removed. This reduces the size of the on-disk catalog greatly. For catalogs which haven't been used for a set period, you can remove the catalog altogether.
Bear in mind that if you remove catalogs, and you need to restore data, then firstly you might not be aware that the backup exists (as Search Catalogs won't reveal anything), and secondly that you will need to re-catalog the media (to import the media-based catalog to the local catalogs) before you can select files for restore. Cataloging tape-based media can take a considerable time, depending upon how many resources are backed up on the media.