You have a finite amount of cones in your eye that see colors. When things are far enough away they blend together.

Imagine a chain link fence. If someone is standing against it then you can see them through a bunch of the holes. If they walk further and further away you'll see them through less and less holes and eventually it may look like they're visible through only one.

Now, imagine they're holding a poster board with a red, blue, and green rectangle. When they're against the fence, this is like being close to the TV. Imagine the holes in the fence as come cells in your eye. Each cone in your eye is stimulated by a single sublixel. As it moves back, the cones are stimulated by multiple sublixels. Once it's far enough back so that a cone is stimulated by all three then the illusion is complete.

Now, it could be that this is one of those weird things that happens with how your brain perceives signals from your eyes and the illusion happens even before that, but I can't remember.