A 'Game boy Advance' ROM, or Gameboy Advanced ROM for short, is just what it says: the file that contains all of the data for a game. So if you think about it as an .exe file, then a GBA R rom would be the .exe file to a Gameboy Advance game.
When you upload the .gba file to your computer, the file is often uploaded as a zip - which means all of the files (including directories and other files) inside will be compressed to make one big file. That's why 'Game boy Advanced ROM' is often written as 'Gameboy Advance ROM' because the '.gba' file became known as a Gameboy Advance ROM.
The best game for the Gameboy Advance is Zelda: The Minish Cap. However, since that doesn't help you much because I've just given you one game, I'll give you a few more:
Check out some more Gameboy Advance games! If you like video games, chances are that you'll like one of these GBA games.
The best, most recommended Gameboy Advance emulator is Visual Boy Advance (VBA). It is stable and has good performance for almost every game. There are also tons of plugins available so you can change the looks/controls of VBA to your liking.