It is a vent line. It is to allow air to escape the rear axle and it heats up and expands, instead of building pressure inside the axle that could blow out seals.
The gear oil expands and contracts as it heats and cools so this hose lets air in/out. You should replace the hose and run it up high somewhere on the frame. If you haven't driven through any deep water or mud you might be okay, but if you have it wouldn't hurt to pop the cover off the axle and check to make sure the fluid is still good.
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