A wave is something that moves along and has high points (crests) and low points (troughs). If two (or more) different wave trains pass over one another the crests and troughs can add together to make bigger crests and troughs, and a crest and a trough can add together to produce zero. So if light is a wave phenomenon, then two light sources produce waves that in some places produce large amplitudes and other places produce zero. When to point sources of light are projected onto a screen this wave interference effect produces alternating light and dark spots. This demonstrates the wavelike nature of light.