Welcome Mike. I had the same question a few months ago. That connector is a big plug connector and the rest of the orange bit comes out of the black part. It is the connector for the O2 sensor. The other pigtail with 2 wires is only used for California cars where the O2 sensor has a heating element so the O2 sensor works faster and controls emissions better. Mine isn't connected to anything.
My connector was also broken so I followed post #6 at
944 Forum - Broken O2 sensor wire connector? to re-connect my O2 sensor. I think that it works now. Others may have other advice on re-connecting it. Good luck!