To build and run MAME 0.227 on Big Sur, updating your installed SDL framework to the new 2.0.14 release is required for M1 machines. It's recommended but not necessary on Intel if you're already up and running.
Get the DMG here: http://www.libsdl.org/release/SDL2-2.0.14.dmg
Open it, then open a Finder window to "Macintosh HD" or whatever your HDD/SSD name is (you may need to open the Finder's preferences and select Sidebar and then enable it for it to be shown) and open the Library folder. Drag the SDL2.Framework folder into the Frameworks folder, and then follow the normal Mac build instructions.
The first time you run MAME after updating SDL on Big Sur (or the first time you build/run MAME on a new machine), you'll get a security error popup. While that error is up, open System Preferences, select Security & Privacy, and go to the General tab. You should see a warning that libSDL2 isn't signed and a button to allow it anyway. Click that, close System Preference, and close the warning that popped up. Run MAME again and you'll get a similar warning, but now it will have an Open button. Click that, and macOS will remember that you're OK with running MAME and will no longer bother you.
Currently, certain games will be slower or not run properly on M1 machines because we don't yet support ARM for our dynamic recompiler (also known as a JIT). In extreme cases like NFL Blitz MAME will lock up and have to be killed, so be careful with post-1995 3D games. The vast majority of games and systems in MAME should run well on M1/Apple Silicon however.