Name this part

I will give my best explanation.
**a set of wires attached to the battery (hot terminal) to the auxillary battery
**it has a plastic red cover over the connection
**it got loose one time and my car totally died while driving, my husband tightened the connection and it worked fine
**now my headlights are dimming when I use electrical stuff - the more I use the dimmer they get (radio, wipers, blower.)

could this mystery part be the culprit?