What is this strange, swirly vortex thing?

I'm seeing these weird miniature black holes all over the place, but I can't seem to interact with them in any meaningful way.

Jumping through them or trying to interact by pressing UP does nothing. None of the NPCs seem to take notice of them, either. What is their purpose? Do they become significant later on?

Solution 1:

This post on the developer's forums has hints for stuck players. It suggests those objects do indeed have significance, and that in order to interact with them you need to use an item you can collect in the game.

The post contains more information, but may also contain spoilers. Read at your own risk.

Edit: In case you don't mind spoilers. ;) These things are:

Warps!

To use them:

To warp, use your bottle on the warps, then jump in once you've activated two or more.