That mighty V8 burns petrol to propel the car. It is pumped from the tank to engine with an electric fuel pump. The fuel is ignited by electric spark plugs. This process is controlled by an engine management computer, which uses electricity. The mighty V8 puts its power to the road through a gearbox. If this is an automatic 540i, there is another computer that tells it when to shift gears. This is also powered by electricity. There are lots of other things in the car that uses electricity but the above are the most important ones involved in keeping it mobile.
The alternator also charges the battery while the car is mobile, but that is not its only function. It converts petrol into electric energy, of which modern cars need quite a lot. The electricity in the car comes mostly from the alternator when it is running. The battery takes up a bit of the slack, but it is mostly there to get the engine started. Or so you can listen to the radio while you clean the interior.
When said alternator stops working, a little red picture of a battery appears on the dashboard. Or is supposed to, anyway. If this did not happen, you may have other issues as well. In this state, the electricity comes from the battery only. It is only a matter of time before it goes flat and the mighty V8 comes to a halt.