Two waves interfere when they run into each other.
The barrier reflects waves that run straight into it. It acts as a wave source and sends wave pulses back up the page towards the incoming waves.
Imagine a loose string tied to a wall. Someone sends two consecutive pulses along the string towards the wall. The first pulse gets reflected right away. It will travel backward towards the person holding the string. Along its way, it will run into the second pulse. The two pulses will interfere. The wall will make the reflected pulse out of phase with the second one. They will end up creating a destructive interference.
So is the case with the water waves running into the barrier. The barrier will send incoming waves back toward where they came from. Reflected waves interfere with incoming ones.