Falling Platforms, much like the Loose Platforms from Spelunky HD, are platforms that will fall when touched. They are commonly found within the Volcana.
Loose Platforms are unstable ledges that will fall straight down shortly after the Spelunker hangs on them, or something walks on them. The platform will break upon touching the ground.
If they give way while you're standing on them, they will often drop you into hazards like Lava, or a Robot. They will also deal 2 damage to anything they hit on the way down, so be cautious of loose platforms suspended above you. If a loose platform lands on a Robot, the robot will explode shortly after.
As there is a short delay before the platform falls, they can be used to cross large gaps, namely lava pits, if you move quickly enough.
You can also ride loose platforms to negate Fall Damage by standing on top of it or holding onto to the side, but always check where you're going to fall beforehand. You can jump off at the last moment to land safely if necessary.
Platforms suspended above enemies can be used to kill them by knocking it down while they are directly below it.