Occasionally you will see a small present icon, that looks somewhat like the present in the world select menu for the "Bonus Levels". If you click it, you will receive a message along the lines of "Congratulations! You may now play the bonus level!" and the associated bonus level will unlock.
For example, this is one on the game's "About" page (top-right corner):
I haven't kept track of exactly where they are, but aside from the above one (which unlocked Bonus #1 for me), I think some are inside levels and some are on the level select screen - IIRC one was on the second 'screen' of level selection in World 2.
As a side note, each present appears to be associated with a specific bonus level, because I had the second one unlocked for a long time before I realised this was the trigger.