The add on to the Red & Blue Series, Yellow is a game that has more relevance to the TV show.
The overall game is fundamentally the same. The aim of the game is for yourself, a Pokemon Trainer, to cover the entire island of Kanto trying to collect the best and baddest Pokemon along the way and defeat the eight gym leaders that stand in your way to facing the Pokemon Elite League and making you ultimate champion of the Pokemon world.
Technically this is a cheap way to plug the enthusiasm shown towards Pokemon and was a way to make money without a sequel put in place. The only notable differences between the Red & Blue versions and this Yellow versions is that Professor Oak gives you an unruly Pikachu to tame - one who, like in the TV show doesnt like to sit in a Pokeball and thus follows you around on foot.
The only other notable changes are that Gary, your sworn nemesis, starts the game with an Eevee and the game introduces Jesse & James, better known as Team Rocket.
Apart from this and a few extra pokemon that can be caught without the need of trading with your friends then there is little more to offer, but a good GB game nonetheless that is sure to keep you occupied.