That is the connection for either the throttle "pull" cable or the choke cable. I suspect it's the latter but I'd need to see for sure which side of the carb rack it's on.
Can you find the piece that broke off? If you can, there's a chance it could be soldered or brazed back into place. Or reattached with JB-Weld if you don't have access to more skookum repair methods.
If you can't find the bit that broke off, you're either going to have to disassemble the carb rack to get that part out for a more professional repair (like going to a machine shop that has a TIG welder and can reconstruct the aluminum and drill/ream a new hole) or find a used replacement part. Like dirtdigger said, a new rack of carbs is likely the easiest way to get hold of that part. Unfortunately.