What is negative current?

understand that voltage is relative to ground,

I prefer to disagree. A voltage is against a reference point. Often that reference point is ground but not always.

Taken the above into account your current is defined the same way.

Take a pin/port of a component or circuit. You can now define the current going into that port/pin as positive from which it follows that if current comes out of that port/pin the current is negative.

It means current can flow in any direction through the device.

Just like with AC mains voltage will alternate polarity over a load, the current flows either clockwise or counter-clockwise direction in the loop via load.

Electric current, in a physical sense, is the rate of flow of electric charge indeed. But charge can flow in one direction or in the opposite direction. That's the reason for positive or negative current: it's a matter of how you set your reference.