The levels don't unlock
All the currently available levels are represented by a number or a lock icon. If you see "Coming soon" or "Coming later", none of that chapter is available yet. However, if you beat all of Business Guy's levels, you'll unlock one "All Characters Level". That is currently the only content that can be unlocked. If you beat 1-5 of Irresponsible Dad's levels, nothing unlocks, but we hope you feel a strong sense of pride.
Making new content has been a painfully slow process for us, but we're in the process of completing that chapter and subsequent chapters.
If you like, you can create your own levels in the editor and then send them directly to friends through email or iMessage.