From the Super Mario Wiki
Bomps (called Sliding Stones by the Prima guide and Pushy Walls by the Nintendo Power guide for Super Mario 64) are a sub-species of Thwomp that first appeared in Super Mario 64. They are living, pushing, protruding stones that act as obstacles in many games. Their name is a pun on "bump" and "Thwomp".
Super Mario 64 / Super Mario 64 DS
Bomps made their first appearance in Super Mario 64 and its Nintendo DS remake Super Mario 64 DS in the course Whomp's Fortress. At the beginning of the course, they go through a pattern of pushing, trying to shove Mario off a cliff and subsequently making him fall to his death. They also appear in other levels, such as Lethal Lava Land. The beginning and end Bomp in Whomp's Fortress are thinner than the center Bomp. Their eyes have a blue outline with blue pupils. The thick outline around the eyes gives them the appearance of protruding outward. In Super Mario 64 DS, the eyes were removed. They can also be destroyed by a character having been powered up by a Super Mushroom.
Super Mario Galaxy
Bomps also appear in Super Mario Galaxy but with a different, more Thwomp-like look and face. They first appeared in Buoy Base Galaxy and later appeared in the Freezeflame Galaxy.
Super Mario Galaxy 2
A Bomp in Super Mario Galaxy 2
In Super Mario Galaxy 2, they appear with the same role and appearance as in Super Mario Galaxy. They appear in the Fluffy Bluff Galaxy and the Throwback Galaxy, which is a remake of Whomp's Fortress. In the Fluffy Bluff Galaxy, Bomps can assist the player in climbing the slope where they are located, but in the Throwback Galaxy, their purpose is more like that of an obstacle.
Paper Mario: Sticker Star
Bomps make an appearance in Paper Mario: Sticker Star in the Chomp Ruins. In the game, they are made out of cardboard instead of stone. They come out from waterfalls and double doors.
Mario Party 10
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Bomps made their Mario Party series debut in Mario Party 10 in the minigame Cliffside Crisis, where they serve as both obstacles and platforms for the players.
Names in other languages
||Comes from "empujón", the Spanish word for push.