Mariokart billboards are a specific type of axis aligned billboards which represent fake 3D objects, the kind of 2.5D that Mariokart on the Super Nintendo used with its Mode 7 trickery.
The idea is that you take a texture like this leaf:
Useless with today’s hardware you say? Not so! The technique allows you to render tens or hundreds of thousands of particles as a huge cloud of debris which looks 3D from a distance, giving cool explosions which work on even the most modest hardware:
Or flip the axis 90 degrees for cartoon rain: