Which term describes the ability of a receiver to detect the presence of a signal?
Why Sensitivity is the measure of how weak a signal a receiver can still detect and turn into usable audio. It is usually specified in microvolts or dBm for a given signal-to-noise ratio, so a receiver rated 0.2 microvolts is more sensitive than one rated 1 microvolt. It depends mostly on the gain and noise figure of the front end stages.
Watch out Selectivity is the other common receiver spec, but it describes how well the receiver rejects adjacent signals, not how weak a signal it can hear. RF gain is just a front-end level control, and total harmonic distortion is an audio or transmitter purity measure.
Sensitivity = Sense the weak signal. Selectivity = Select one signal out of many.