Water waves travelling towards along the water container are reflected off the walls when they reach either ends. Incident and reflected waves thus superpose and interfere with one another. A standing wave of significant amplitude can be formed only when the water waves have certain “correct” wavelengths.
Since water waves reflect off a wall without incurring any phase change, displacement antinodes are formed at the boundaries. What was shown in the video were the 1st, 2nd and 3rd harmonics.