I'm familiar with the term "gain" used in sound and music, but I'm having difficulty finding the definition in electronics. I'm seeing the term low gain and high gain being used in the description of the Panasonic Grid-Eye infrared sensor. What exactly is gain a measure of in electronics?
Gain is just the ratio of two quantities. When talking about circuits, it's almost always the ratio of some measurement of the output of a circuit or component to its input.
As Olin said, the most common case is the voltage gain. That is, the ratio between the voltage amplitude of the output signal to the input signal.
Another common specification is power gain, the ratio of the output power to the input power.
But some circuits are best characterized by a current gain. Some (transimpedance amplifiers) are best characterized by a transimpedance gain --- the ratio between the output voltage and the input current.
Another common usage of the term gain is in antennas, where the gain of an antenna is "the ratio of the power produced by the antenna from a far-field source on the antenna's beam axis to the power produced by a hypothetical lossless isotropic antenna, which is equally sensitive to signals from all directions." (per Wikipedia)
"Gain" is usually voltage gain unless otherwise specified. Keep in mind that power gain is proportional to the square of voltage gain.
Sometimes gain is specified in dB, which is actually a way of expressing power ratios. A dB is 10*Log10(power1 / power2). This becomes 20*Log10(voltage1 / voltage2) if the two voltages are at the same impedance.
It's actually typically exactly the same thing as in audio. Or, rather, the audio use of "gain" (for signal voltage amplification) derives exactly from the electronic "voltage gain" used in amplifiers.
This means that the dB ratings of gain mean the same thing -- 20 dB means a factor 10 in voltage which means a factor 100 in power.