Let me show you my Pokemans, in colour!
First off the obvious one, this game is (partly) in colour. You no longer have to put up with seeing your little Pokemon friends in poor old black and white all the time. Another new addition is that Pikachu is given to you, the player, at the start of the game; and your rival Gary starts off with an Eevee instead of Charmander, Squirtle or Bulbasaur. Some area layouts have been changed from the previous titels, and Pokemon can now be located in different areas.
The modifications are to resemble the animated series as much as possible. Encounters with Team Rocket now pit you against those rogues Jesse and James, and Pikachu follows you around on the screen instead of staying inside his Pokeball. Speaking of Pikachu staying out of his 'Ball, you can check up on his status by facing him and Pushing A. A small box will appear in the center of the screen with Pikachu making a facial expression. These expressions indicate whether or not you need to spend some more quality time with him to make the fella happy. This can be done by sending him out into battle and being kept well with Potions. He also stars in a surfing game! Just don't ask why....
As for Gameplay, it's pretty much the same. Run around in grass, capture Pokemon with Poke Balls, train them up to higher levels then battle trainers and gym leaders until you reach the Elite Four. It may sound simple but believe me, it'll take you a fair amount of time to become the Pokemon Master. And once you've done that, you'll want to go back and catch all 151 Pokemon. Have you got some 30 - 40 hours to spare?
The visuals are very similar to Red and Blues with a little upgrade in them here and there.
Yellow is a fun Pokemon game, but when it first came out it was just to keep you busy 'til the real Pokemon games to come were released.