You have been able to use the Apple Watch to unlock your Mac for a couple of years. In the Security & Privacy pane of System Preferences, you can check a box to allow this to occur. When you’re wearing your Apple Watch, and it’s unlocked, pressing a key on your keyboard or clicking your mouse tells the Mac to look for the Apple Watch to authenticate you. This was the single feature that got me back to using the Apple Watch a couple of years ago after having worn the device off and on.
Now, in Catalina, this goes one step further. If you have turned on the above setting, you can use your Apple Watch to enter your password when you need to authenticate to perform administrative tasks. For example, if you want to delete files in the system space, applications installed via the Mac App Store, or access secure preferences panes, you must enter this password.
Now, you’ll see a dialog like this:
Double-press the side button on your watch, and, boom! It’s done. This will save a lot of time when performing this type of operation, and it allows you to create a more secure password, because you won’t need to type it as often.
Note that on a Mac with Touch ID, this latter technology seems to overrule the use of the Apple Watch. Here’s what I see on my MacBook Pro:
I guess this makes sense; it defaults to the closest method of authentication available to the device, and using Touch ID is even a bit quicker than using the watch.