What does it mean when your car dies and your battery and oil light comes on?

Warning Light Operation

Both the "battery" and "oil" idiot lights turn off when the engine is running and thus indicates that the alternator is putting out current to recharge the battery, and the oil pump is circulating enough oil to maintain a safe oil pressure to protect the running engine.

When your vehicle "dies," that means the engine is not running, and thus these indicator lights tell you that the alternator is not putting out current, and the oil pressure is below a preset level.