Green Shells are items featured in the Mario series and the most common type of Shell. They're normally placed on the backs of Koopa Troopas, though an opponent can come in possession of it by stomping on the turtle's head, where the shell will then pop off (it should be noted that in the real world, the shells are connected to turtles and cannot be removed, though the world of Mario allows for things such as this to happen).
Following this, you're allowed to either kick it or pick it up depending on the video game. In the original Super Mario Bros. for the NES you were only allowed to kick it, where it would then ram into enemies, thus killing them. The player could perform an interesting trick in the game where they could earn an unlimited amount of lives by jumping on a shell placed on a brick pyramid. If done correctly, they would continue to jump on it non stop giving them tons of lives.
In the Mario Kart series, starting with Super Mario Kart for the SNES, the player could find Green Shells inside of item boxes. They were most common with people in first place, as they were considered as one of the least helpful items in the game. Once you got it, you were capable of shooting it at an enemy, though unlike the Red Shell it would not home in on them. However, Green Shells could bounce of walls and Red Shells cannot.
In Super Mario 64 for the Nintendo 64, Mario could ride on top of shells and also ram into enemies to defeat them. This could also be performed on top of water for quick traveling. In Super Mario Galaxy for the Wii Mario could use the Green Shells under water to travel more fast than before. Red Shells were faster, however, and Gold Shells would give the player a Star.