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.