It was the battery life wot won it
The relatively low spec hardware had one massive advantage over the rivals (Game Gear / Lynx etc) which was the battery life. You could easily get several days of solid play out of a set of 4 AA batteries, and even as they started to die you could still play by judicious use of the contrast control.
I vividly remember the craze in these at school. One friend proudly brought in a Game Gear (I think he even had the fabled TV tuner attachment) but the thing was dead by lunchtime, whereas those with Gameboys could play all through lunchtime and still be playing on the way home!
The other big plus was the multiplayer mode, and a stroke of genius was making Tetris (which you wouldn't think of as a two player game) multiplayer, so everyone could try it. It was the first time I'd ever really experienced this and it was great fun.