Why do the Omega Seamaster watches have a second crown close to the top of the watch? What is its function?

This is a helium release valve.
The purpose and function of the helium relief valve is a common point of confusion. It has nothing to do with normal underwater diving. Neither does it have anything to do with the depth rating for a diving watch. Helium does NOT seep into the watch while the watch is in water at any depth!

To put it simply, you can completely ignore a helium relief valve. This feature is not used in any way with any form of normal SCUBA diving or anything else that involves less than a multi-million dollar deep sea exploration project.

SCUBA diving activities normally occur at depths of no more than 120 feet. At 250 feet, air becomes toxic due to changes caused by the high pressures at such depths. For those who do very deep sea research, they often use diving bells, dry dive suits, and other types of very deep ocean exploration vessels. In some of these, a highly helium-saturated atmosphere is used to avoid the air toxicity effect.

The purpose of a helium release valve is for people who wear their watch inside the helium-saturated environment for an extended period. Because helium is the smallest atom, it will seep through the watch's seals under the high air (not water) pressures in this environment. If the watch stays in this environment for an extended time, helium will continue to seep in to the watch until the air pressure inside the watch (initially surface air pressure) equalizes to the air pressure in the environment.

This becomes a problem when the vessel is brought back up and depressurized. The helium which seeped into the watch over a couple of days, cannot seep out any faster. The excess pressure inside the watch needs a way to release faster than it seeped in. It is only in this situation that a watch needs a helium relief valve at all. If a relief valve was not on the watch, the excess pressure would likely escape by pushing the crystal out.

But, unless you are in this exact situation, you should never keep this valve open. While the watch is designed to maintain most of its waterproof abilities even when the valve open, it still serves no purpose and increases risk of damage to the watch to do so.