When anode is positive and cathode is negative then there is expand in the depletion region thus the diode acts as forward bias. When anode is negative and cathode is positive then there is breakdown in the region that is called as reverse bias.
In forward bias, positive terminal of the device is connected to positive terminal of the battery and negative terminal of the device is connected to negative terminal of the battery.
Whereas as in reverse bias the connections are interchanged,i.e positive(device) to negative(battery) and negative(device) to positive(battery).
Forward bias is a PN junction bias which allows current to flow through the junction. Forward bias decreases the resistance of the depletion layer.
Reverse bias is a PN junction bias that allows only leakage current (minority carriers) to flow. Positive polarity on the n-type material and negative polarity to the p-type material.