2011 Chevrolet Malibu - what’s service ESC?

Traction warning lights stay on also says service esc. What does that mean?

Exactly what it says: It means the traction control system needs repairing.

Here’s a link to the Owner’s Manual that came with your car when it was new. 2011 Owner’s Manual

Look to Page 5-19 for this particular warning light.

Electronic Stability Control.