Air has weight. The column of air above you exerts about 14.7 PSI upon everything on earth at sea level. It's what keeps blood inside your body, and allows you to breathe.
The carb bowl vent allows this pressure onto the surface of the gas fluid in float bowl.
When the engine's piston fall while the intake valve is open, air rushes in to fill the vacant volume, creating pressure negative to normal atmospheric pressure. The fuel jet orifice now experiences a differential pressure across it and passes fluid, to be mixed with incoming air, into the engine cylinder.
Without a bowl vent, there would be no physical way for the fuel jets to deliver fuel, in the existing design.
Cheers,