A function called ':' is defined. In its body, it calls itself twice at the same...

A function called ':' is defined. In its body, it calls itself twice at the same time (':|:') (piping the output of the first call into the second, which doesn't do anything useful) and sends these calls to the background ('&'). After function ':' is finished being defined, it is called.

The first call spawns two clones. Each of those spawn two more. Etc.