The threshold pump power of an optically pumped laser is the value of the pump power for which the laser threshold is just reached. At this point, the small-signal Gain equals the losses of the laser resonator. A similar threshold exists for some other types of Light sources, such as e.g. Raman Lasers and optical parametric oscillators.
For an optically pumped laser, the definition of threshold pump power may be based either on the incident or absorbed pump power. For applications, the incident pump power may be more relevant, but the Threshold Power with respect to absorbed power can be interesting e.g. for judging the gain Efficiency of the gain medium.