The term "Mae Wests" refers to the vest-like yellow inflatable floatation device frequently worn by aviators.
In its dormant form it appears rather flat.Down by the waist are two CO2 cylinders which have short toggle ropes attached.If needed the downed aviator can pull these ropes and a small pin is pushed into the cylinder releasing the "bottled air" into the flat compartments of the vest.This done the vest expands creating a floatation device.
Visually it makes one appear "well endowed" in the chest area, which in the 40s, was equated with the actress Mae West "Come up and see me sometime..." who was naturally well endowed!
There were other types of flotation devices available for other waterborne applications.Submariners had a similar "Mae West" also worn round the neck which was gray in color.On amphibious operations, landing forces were issued with a floatation device in the form of a belt.Much easier to dispose of once on land.This also operated with CO2 cartridges, and were activated simply by squeezing the side of the belt which would expand around the wearer like an inner tube.
Sailors and other shipborne personnel would wear kapok filled life jackets which are less analogous to the conventionsal definition of the inflatable Mae West vest.Seaborne life jackets were stuffed and available in deck lockers in the event of emergency.
I would like to sent compliments to the members of your mother's generation for the products they built in the 40s---particularly these inflatable Mae West vests.In 1995 a group of friends and I, attending an airshow/pool party, all brought out our then 50 year old Mae Wests and jumped into the pool sinking to the bottom.We all pulled the toggles on our vests and everyone of us rocketed to the surface.They still worked!!Fantastic.