Aight, let me take a shot at it.
An unobserved stream of light/electrons passing through two wavelength sized adjacent slits results in an interference pattern (bunch of bright and dark spots) suggesting wave nature of particles.
But when observed with a detector to see if one particle is being split across two slits (which it didn't) it resulted in just two bright spots along the slits, indicating the particle nature.
So, that shows there is wave/particle duality to matter. But why it shows different results in different conditions is unexplained so far.
Now go read up the Wikipedia page until you're convinced.