This is a resonance effect, and you see it a lot in nature. What’s happening here is that as the metronome pendula swing back and forth, their combined motion induces a resonance in the wood/can structure. Think of it this way: two metronomes perfectly out of synch with each other (one swinging left just as the other swings right) would exactly cancel each other out. But little differences add up, and the leftover motion is what sets the platform moving. It starts to rock back and forth.
But the platform is inducing a force on the metronomes, too. If the platform is moving to the right as a metronome pendulum is swinging left, it feels a force, a force that makes it move even more to the left. As long as they are out of synch this force will act on both the platform and the pendula. Eventually, as the frequencies of both the platform and the metronomes change, they reach a point where they are in synch. Once that happens, there is no more residual force, so they stay beating in time with each other.
Resonances are everywhere. Ever hit potholes in a road that are spaced out so that you hit the next one just as the car is coming back down on its shocks from the last one? Or driven on a dirt road with the ripples in the middle? Ever whipped a rope back and forth and got those sinuous patterns that seem stable? Ever seen the gaps in Saturn’s rings, caused by the moons orbiting the planet? Ever pushed someone on a swing, getting them going higher and higher?
Resonance, resonance, resonance.
Science is everywhere, my friends. And it rings true.
