From the Super Mario Wiki, the Mario encyclopedia
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A Squarp Hole is a small circular opening in space in Super Paper Mario. They are violet-colored worm holes with triangles and circles surrounding them. Their name is a portmanteau of "Squirps", "warp" and "worm hole". They have a Kaleidoscope effect to them in appearance. They come in three variations.
Squarp Holes can only be found in Chapters 4-1 and 4-3. In Chapter 4-1, after Mario meets up with Squirps, Squirps creates one using Mario's power (holding down and letting go to charge it), and Mario then uses many other Squarp Holes to reach the end of the level. In Chapter 4-3, after Squirps demands food, Mario navigates a maze of Squarp Holes in order to reach a convenience store in space.
In the game, they are used to transport characters from one part of the level to another, much like Warp Pipes in many other Mario games. It is unknown as to how the other Squarp Holes aside from the one created with Mario's power were created. It is possible that the power of the Pure Heart was used, or that the power to make Squarp Holes naturally occurs in Squirps' family or species.