That, my friend, is the crankcase breather hose which is connected to crankcase breather. Blowby from combustion chamber enters crankcase (past rings/valve guides) and pulled out of crankcase by partial vacuum in carb via this hose and is then re-burned. This system actually adds to combustion chamber deposits (carbon build-up).
This hose was added sometime in the '60's and before that crankcase gases were just dumped into atmosphere.
If you were to look behind breather you will find valve springs and tappets and a hole which leads to crankcase/oil sump. Equivalent to a pcv valve found in a car engine.