For maximum performance, we recommend you save your catalog on the fastest drive available to your computer. This will typically be the boot drive ('Macintosh HD' on MacOS and the C drive on Windows).
You can archive your photos on external drives, such as network-attached storage (NAS) or external backup drives if you wish. Your Catalogs do not need to be on the same drive in order to be able to search and find your photos. The catalog contains a database and (optionally) previews rather than the photos themselves.
We do not recommend that you ever store catalogs on NAS drives. Similarly, we do not support storing catalogs on Dropbox or other cloud drives. This type of connection is slow, and we do not support sharing catalogs with other users at this time.