Collimated light waves come from the laser and pass through a pair of narrow slits in the slide; the light passes through and then projects on the distant screen. But light travels as an electromagnetic wave, so when the light comes out of the two slits, it forms two wavefronts, just like ripples from two stones dropped in a pond. These two wavefronts can interfere with each other, as we can model with this pair of overlapping concentric circles. Where two peaks or two valleys of the wave pattern line up, they add together, interfering constructively; when a peak and a valley overlap, they cancel out, interfering destructively. The same happens with light waves; the light from the two slits overlaps, and creates a pattern of bright spots (constructive interference) and dark spots (destructive interference). The spacing between the bright and dark fringes ultimately depends on three things: the distance between the slits and the screen, the wavelength of the light, and the spacing between the two slits.
Two simulations that can be of value in introducing this topic: