[RedBank16]

Mike1010 is correct.
The valves were meant to stabilize the the pressure inside the boots when in flight. Most of the boots with valves had the words "keep closed unless in flight" surrounding the valve. If you left the valve open and water got inside, you ruined the boots. That is because the boots were rubber inside and out, with a 1/2" wool felt insulation
The boots were developed by the U.S. government during the 1950's, and were used by the military into the 1980's.
They were available in black (for cold, dry climate) and were called "Mickey Mouse" boots, and white (for cold, wet climate) and were called "bunny boots". They were both available with and without valves, but the boots with the valves were rated for colder climates, and the white boots were warmer than the black.
The white boots had a rigid sole, and the black boots had a flexible sole.
The boots were meant to be worn with one pair of military cushion sole socks.
I have the black boots both with and without the valves. I have used the black boots without the valves on a hunting trip in -21 degrees F!
The white boots without the valves are the hardest to find.