I broke the wire that is connected to 12V battery. What it is?

The battery should have a fat wire connected to the negative terminal, a fat wire connected to the positive terminal, a skinny wire connected to I forget which terminal, and a small black hose that runs from the battery to outside.

The fat negative wire is your ground to the body. The fat positive wire runs up front and powers all the small stuff, the skinny wire is what the car uses to monitor the charge state of the battery, and the hose is a safety vent in case the battery overcharges and starts outgassing, so it just vents outside. I don't know what would be connected to the tie down bar.

someone has retrofitted a yellowtop battery into your car. It may not have a connection point for the hose. They are a good battery and should not fail weekly. Have you checked for a parasitic drain?

 

If you're talking about the wire attached to the thing that sits on the battery hold-down bracket, the thing is the temperature sensor (allowing the car to adjust the charging to the temperature around the battery) and that's what the wire is for.

 

Eco is missing from the display? Solder it back