The term "bias" is very general and describes a stable operating point in a circuit. Often for a diode, it refers to a "reverse" voltage where the diode is "off" and not conducting. So, for a diode, the forward voltage is the voltage across the diode when it is "on" and conducting normally. It is the region in the upper right quadrant of the IV curve. A bias voltage is a voltage across the diode when it is "off" and not conducting. It is the region in the lower left quadrant of the IV curve. Another way to think of a diode bias voltage is a "reverse" voltage. So, there are forward and reverse voltage. A "Bias voltage source" for a diode would be a voltage source which puts a stable, reverse voltage on the diode.
One use of reverse biasing a diode with a voltage source is in clamp circuits which provide overvoltage protection. Normally, the diode is off. However, if a signal voltage on the other side of the diode exceeds the bias voltage plus the diode forward voltage drop, the diode turns on and limits the signal voltage. Also, photo-diodes are reversed biased to enhanced their light response.