2000 Explorer: on the drivers side is what looks like a vent hose coming off the axle housing. Is it a vent and why??

 

It's a vent, and it's so as you're running down the highway the rotating parts in the rear end do not build up so much pressure that is forces fluid through the axle seals or pinion seal. I want to use the term "cavitation" but I have not looked up the definition to see if that's an accurate description of what happens to the fluid when the gears and bearings are spinning.

-Rod

 

Interesting. The rubber hose had broken off. Thx Rod

 

It allows the axle to "breath". Temperature changes would otherwise cause the air in the housing to expand or contract causing either pressure or vacuum within the axle housing.

The vent allows the internal pressure of the axle to remain the same as outside pressure.

It's not cavitation.