From the Super Mario Wiki
Raining Debris are molten rocks seen falling from the background of volcano-based levels. They first appear in World 8-8 of New Super Mario Bros., which is a level with many Kab-ombs. These rocks destroy blocks and set off the fuses on Kab-ombs, not to mention hurting Mario or Luigi if they touch one. Mario and Luigi can, however, take refuge under the dark floating platforms that the debris cannot penetrate.
Raining Debris reappear in New Super Mario Bros. Wii, and are mostly found in World 8-1. In this game, they are much harder to dodge as the player has to jump through a lava-filled land with mostly small platforms to jump on, drifting poisonous clouds, and rising lava spouts. Larger forms of Raining Debris also appear, and can plow through several blocks before landing, in addition to taking up valuable space.
Raining Debris return in New Super Mario Bros. U. In this game, they now resemble fireballs, but their function in this game is the same as in the prequels. Raining Debris are found in two stages of Peach Castle: Meteor Moat, and the secret level Firefall Cliffs. Bowser's fireballs in The Final Battle are identical to Raining Debris. These obstacles also appear in the challenge, Cloudy with a Chance of Fire.
Raining Debris also appears in Super Mario 3D World, marking their first appearance in a 3D Mario platformer game. They look similar to their appearance in New Super Mario Bros. U, and act similarly to the previous installments, though they now also create molten fire puddles that will damage the player if they touch it. They only appear in The Great Tower of Bowser Land, where they are once again expelled by a volcano in the background, and in Hisstocrat Returns and Boss Blitz, where they are generated by Queen Hisstocrat.
In Paper Mario: Sticker Star, Raining Debris are known as meteors and are only found in one level, Rugged Road. They can still hurt Mario if he touches them, but now they can also harm him if he gets caught in the spot where the debris landed for about one second. They may also try to push Mario into lava and will always home in on him.