How does a stench pipe work

A "stench pipe" is a vent pipe.
On a two bath house, as a rule you have three vents. One each on a bathroom lavatory that vents the group, and a kitchen sink vent. If you have a laundry room that could be another vent. Sometimes we tie them all togather in the attic so that we only have one pipe coming out the roof. This is called reventing. A vent that does not terminate through the roof is called a local vent.This is a vent vent that terminates inside a wall. This is a mechanical vent that is spring loaded so that it lets air in to vent but stops sewer gas from getting out. This vent is called a AAV or Air admittance Vent. A plumbing drainage system has traps on each fixture. These traps keep sewer gas from escaping into your house. On a unvented system the water draining sets up a suction that syphons the water out of the trap letting sewer gas out into your house. I have tried to explain how vents work and the different kinds. You asked how important venting is. Vents are necessary for a plumbing system to function.
Hope this answers your question, Tom