Best answer: Fastboot is part of the Android bootloader as well as a program you can run on a computer to communicate with it. You might have seen it in action if you’ve ever unlocked the bootloader or had to manually update a Pixel phone.
A confusing name but a simple idea
Fastboot is three different things with the same name: A protocol for communication between your phone hardware and a computer, software that runs on the phone when in fastboot mode, and the executable file on the computer you use to make them talk to each other.
The file you run on a PC (or a Mac) is nothing flashy. You download it from Google and stuff it in the folder where the Android SDK parts live and it just works. The protocol is automatic and if your phone is in Fastboot mode and you run the file it too just works. The phone part is an entirely different story, though.
Unless you have a Pixel phone, an ancient phone with Nexus branding, or an even more ancient phone from HTC, you probably don’t have access to the regular Android Fastboot mode. Google provides it freely and any other phone maker is allowed to use it, but most have their own version of a way to interface with the bootloader.
That’s a bit of a shame because Fastboot is really powerful. You use it to unlock bootloaders, update software, or even fix a “broken” phone. Of course, that also means you can easily wreck the software on your phone through Fastboot, which is probably why other phone makers use something different.
Even if you do have a Google Pixel phone, you’ll probably never need to use Fastboot. But it will be there for you, just in case.