One tank has the outflow to the filter, one tank has the return from the filter.
The two tanks are connected by a U-shaped tube that's been filled with water and has both ends well below the surface of each tank. This is the siphon.
As water starts to exit the outflow tank the water level begins to drop, creating a lower pressure on that side of the siphon. At about the same time water starts entering the return tank, raising the pressure on that side. This causes water to flow through the siphon from the return tank to the outflow tank to keep the pressure (and water levels) equal on both sides. The rate and direction of flow through the siphon is controlled by the flow to and from the filter — its a system trying to maintain equilibrium.
The big concern is: what happens if the siphon were to ever break (air bubbles collecting in it over time) or clog? (The outflow tank would empty out and not quite half the water in the system would flood over the sides of the return tank, at which point the filter would run dry and you'd burn out the pump -- all very bad things

).
You'll notice most of the posts address these two things, siphon breaks and clogging. RTR has a very clever bleed-off and along with OG favors redundancy. Somefinnfishy mentions keeping the tubes short to minimize the flooding in the worst case scenario. Somewhere in my searching on this I came across someone who mentioned drilling a small siphon-breaking hole near the top of the outflow tube so that if the water level on the outflow tank dropped too far the siphon to the filter would be broken before all that many gallons got out over the side. Somefinn also mentions using an overflow box, which would likewise help minimize potential flooding by limiting the outflow.
It seems to me that there are enough solutions to the potential problems and I'm mostly leaning towards trying a two-tank setup at this point.