[Afrobean]

It was originally a game called Mario Bros. I actually own a copy of it for NES.

Then, it was used as a minigame in Super Mario Bros. 3 in which a player could steal the other player's turn by winning in this game. The players could also steal the cards obtained by completing levels in normal gameplay by hitting the POW brick.

As said above, when the Gameboy Advance came out, it has been included in pretty much every Mario game released for that system (except for, it seems, the rerelease of Super Mario Bros. as a NES classic). In addition, I believe it is possible to link a Gameboy Advance with one of these cartridges with the game to another Gameboy Advance with no game in it and play two player Mario Bros. that way as well.

ps I do believe that the screen shot in the original post is actually from Mario Bros. as a stand-alone game, and not in any of its incarnations as a minigame.