To find Catalog Management, navigate to Catalog>Catalog Management. 

Catalog Management helps with tasks such as moving, adding, and deleting catalogs as well as allowing you to control the size of preview images to save space.
Use the triangles to find more options ext to each catalog.

The Catalog Management dialog also indicates which catalogs need maintenance, for instance after Photo Mechanic Plus has been upgraded with a newer version of the catalog.

Maintenance Options

Forget: The Forget button does not delete a catalog but removes it from the list of available catalogs as if Photo Mechanic has forgotten it is there. Use this to move catalogs to another computer or location. Use Reintegrate Forgotten Catalog to restore.
Rename: Use this to rename a catalog. 

Delete: Use this to delete a catalog - just the catalog, index, and preview images. The original images will remain.
Calculate Catalog Folder Size: See how much disk space is being used by your catalog and stored proxy preview images.
Generate preview & thumbnail proxy images: Check if you want to see previews of images in catalog contact sheets without having to generate new proxies from the original images each time. This is faster but uses more disk space. 

Preview size: Use this to control the maximum size of proxy preview images indexed inside your catalog. If your catalog is taking up too much space, but you still want to see thumbnails, decrease the size of the preview images.
Maintenance: This triangle pulls down database maintenance options. The options are:
Optimize SQL Query Planning: This is recommended after adding or removing a large number of documents to or from the catalog.
Reintegrate Forgotten Catalog: Use this to "unforget" a catalog.
Re-index Catalog: This is rarely needed. See this article on how to use it.
New Catalog: Create a new catalog.
Locate Existing Catalog... Point to a catalog that has moved.

Further reading on tasks that use Catalog Management: