Its part designation is "Bypass Hose". It's function is not 100% clear to me.

However, if you take a moment to analyze it, it seems that it allows for excess water pressure from the high-side of the radiator (driver side) to dissipate into the low-side (passenger side) of the radiator in situations during high-revs.

Another, more simpler reason would be to allow air pockets/bubbles to escape from the high-side to the radiator neck on the low-side.