What is Reverse Current through an Arduino?
It's current flowing "the wrong way".

The electronics inside the main chip are designed such that the + side (Vcc) must be at a significantly higher voltage than the - side (GND).  By significantly I mean 2.1-5.5V higher.

Because of that it is expected that the current will flow through the components in one direction (or in a couple of pre-determined directions depending on settings).  Any situation which causes a reversal of that current through the internals is bad, and as called "reverse current".

It could be caused by something as simple as connecting a power supply backwards, or more technical things like the "Back EMF" from an inductive load (motor, relay, etc) entering a pin that is an output and flowing backwards up to Vcc, or "Back Powering" where the chip is not powered but some external device connected to it is powered, and it "leeches" power backwards through IO pins to power the chip.

All of those situations are bad and should be avoided.