The term integration time is used for radio telescopes and CCDs, for the length of time over which data is collected and combined. Thus 20 seconds of integration time means an image (or even just one pixel, depending upon the set-up) is created by gathering photons for 20 seconds. The 20 seconds might have been dedicated to gathering two images, each with 10 seconds of integration time.
It generally means the time over which an analog signal is converted into a digital count representing an integration of the signal. Such an integration time may be chosen as best to reduce systematic noise and/or random noise. For some objects, minimums for workable integration times can be calculated from the temperatures of the observed object and the observing instrument.
For transients, there is a trade-off of the selected integration time versus sensing the changes that are happening in the same general time frame.