This is in some ways extremely obvious, but I'm still motivated to try to express it:
Humans and other sentient animals experience the world such that some stimuli continue to occur perceptually even once the external, objective stimulus has ended. Our internal perception (memory, imagination, etc.) rings and reverberates and sustains perceptions that occurred once and have stopped occurring–and indeed, parts of our perceptions of the external world are also painted over with reverberations or continuations of perceptions that have ceased to occur.
We perceive, but we perceive not just the external world, but also our internal world, and both of those are also painted over with lingering perceptions (memories) and with models/art/predictions (edited memories).
Sentient beings are beings for whom perceptions linger.