The battery is the reservoir of electrical energy the alternator tops up energy taken out of the battery. Start the engine does the battery icon go out. Put a volt meter across the battery terminals with the engine off, at rest the battery voltage should be 12.6 volts if the battery is fully charged. Now get a friend to start the car while you watch the voltmeter, the voltage reading across the battery should read approximately 14.6 volts if the alternator is charging correctly. You may have some sort of battery draw that needs to be isolated and illuminated. You would need an amp meter disconnect one cable of the battery put your Amp meter in series with the battery cable that has been removed. Note the draw say for example 15 Amps, with the keys out of the ignition, doors closed driver's window down, start removing the fuse links and fuses one at a time until the voltage draw goes away to zero (or near zero). It is that circuit that is causing the electrical draw, then look at a wiring diagram, see what consumers are on that circuit and start to isolate each circuit to see which is the culprit. Most likely you have a failing battery have it charged and tested.
The fuse on your positive battery terminal is blown. It will cost between $10 and $20 from a dealer.