The end of that wire had an end that would plug into that coax "socket". The easiest way to fix this would be to get one of these:
http://www.google.com/products/catal...=0CJIBEPMCMAA#
And then get one of these:
http://www.google.com/products/catal...=0CJMBEPMCMAA#
You put the coax end on the damaged wire and then you connect the two using the female-female adapter. You can get both parts at your nearest Radio Shack, not the cheapest place but if you don't have a "real" electronics distributor nearby it will be the best bet. If your antenna already has VHF & UHF combined then you put one end of the female-female adapter in the wire from the set and the other end in your antenna coax. If you have 2 antenna wires, one for each band, connect them to the screw terminals and plug the wire from the set into that coax connector on the left using the female-female adapter.
Was that clear enough?
Edit: basically, older sets used only the 300ohm screw terminals for antenna connections. Coax was better so set makers started giving an option. The coax coming out of the set is what runs to the tuner. The other stuff is just a built-in 300 ohm to 75 ohm adapter, same as you can buy in the store.