In simple words, Emulator is a virtual machine for your console device. Now What ? You need an Emulator of that console to play that ROM file.
Since you got the concept of ROMs, now you have your favourite game ROM on your system but no console. You can simply select your desired ROM category from above and find your favourite game. Now you know the concept of ROMs, you do not need to go in deep. Now you can download your favourite game ROM file from here and can play your game. Here on, users from around the world have extracted the ROMs file and submitted here. We need ROMs file to play our favourite games.
But now as we are using the virtual tools i.e emulators to replace those console. ROMS is basically a Game file, if you remember the old days when we use to play games on console, we use some sort of cartridge of video games, which is loaded with games software or in other words games ROMs.