What happens when light passes through a diffraction grating?
It gets diffracted.
If the grating spacing is comparable to the wavelength of the light then we should see a "diffraction pattern" on a screen placed behind; that is, a series of dark and light fringes.
We can understand this by thinking of each open slit as coherent source and then at any point behind the grating the effect is obtained by summing up the amplitudes from each. The amplitudes (borrowing unashamedly from R.P Feynman) may be thought of as the rotating second hand on a clock.
Those that come from close by will have turned only a little, those from further afield more. We must then place them heel to toe (as vectors) to find the resultant. For example, two hands that point in opposite directions will cancel, two that point in the same direction will add constructively.
It is then a question of a (not simple, but not overly hard) mathematical calculation to see that at certain points the overall effect is constructive (interference) and so light and at others destructive and so dark.