Sorry if this is stuff you already know. But I need to get my reply clear in my head as well as explaining to you as I don't want to suggest deleting files without backups and some assurance what you're doing is non-destructive.
The lightroom catalog is a database. Fundamentally a list of the locations and data pertaining to your images. It doesn't contain your actual image files.
Lightroom is, at it's simplest, a way of interacting with your images. These images can be in folders on an external USB drive, your local drive, a network drive etc. Lightroom just notes where the files and keeps data about them in the catalog.
So there are two halves to the puzzle.
Lightroom with it's catalog and the real location of the files. Both need to be kept in sync with one another. If you want to change the location of your images, perhaps your hard disk on your Mac is filling up you must do this from within Lightroom. This is the only way it can update the location information and keep the physical location and catalog in sync.
So, where to go from here.
This is what I would do:
1. Get an external hard disk, at least as big as your Mac hard disk (I'd suggest twice the size). Use Time Machine to backup your whole machine (lets call this extHD1).
2. Move the catalog to your Mac hard disk (it'll perform faster from here)
3. Use Lightroom to open the catalog and then use lightroom to relocate all your images to your existing external disk (extHD2)
4. From now on new images get imported to extHD2 and then added to Lightroom.
5. Not forgetting the images on extHD2 will need a backup strategy. Whether included in the Time Machine backup and/or backed up online.
Hope some of that helps