I guess I never really thought about this, but this equation makes a lot of sense. The longer light has to fall on to a surface, the more "energy" and thus exposure that surface gets. And, when the light has more power, the surface also has a higher exposure
You can think of it as a solar panel or a plant. Both draw energy through sunlight exposure, thus accumulating power over time.
If we look at the units, exposure is a bit more intuitive. Exposure time follow seconds (s) and irradiance is (W/m^2). If we multiply the SI units together, we get W*t/m^2 = J/m^2. It is the total energy falling per area squared! The more energy per area the higher exposure!