The new address bar is cleaner and better optimized for smaller screens. Selecting it will pull up a one-pane suggestions interface that scales to your screen size (you don't need to type anything for this to show up). Within this pane, you'll see "Search with" shortcuts (such as Search with Google or Search with Amazon) as well as a list of some of your top sites.
These top site shortcuts will sync with any tabs you might have open, so you can click on, say, your top site entry for Facebook to quickly pull up a relevant tab. Firefox already offered a similar function in the past, but it often required you to enter related text first (starting to type "YouTube" could show you a few shortcuts to your YouTube tabs).
Once you've started typing in the new address bar, you'll notice that the URLs have been shortened, and keyword suggestions now appear in bold. The font size for the address bar and its various suggestions has also been increased, which could be useful for those on high-DPI displays.
In other news, Firefox 75 is now available in Flatpak, which should pave the wave for easier Linux installations. Additionally, "Direct Composition" is now supported for Windows users, which Mozilla claims will boost performance.
If you've never used Firefox before, or you simply haven't downloaded the latest update, you can grab Firefox 75 right here.