The easiest way is to see it as 3 towers, 3 circles and 3 ropes. They are all on top off the table and need to be attached to each other, without any rope crossing one another. This is not possible without working in three dimensions. My player's made this solution with the middle tower being elevated above the red portal.
The red, green and blue lines never cross each other, so this is a solution. Drawing in three dimensions was difficult, but the idea is the red green and blue line are attached to the bottom of the elevated tower.
It's related to a simple logic problem, that's often described a number of different ways. Usually, it's connecting three different utilities (water, power, and gas) to each of three different houses (A, B, and C) with the same caveat: no two lines can cross.
Strictly speaking, the puzzle is impossible when constrained to two dimensions: There is simply no way to do it. The answer usually comes through some degree of creative manipulation of the rules: For example, you can run one utility completely through one of the houses, to supply the next. Nothing in the rules say you CAN'T do this, but most people just assume that's a parameter. They subconsciously handcuff themselves right at the start of the puzzle.
The 3 Towers puzzle, thus, is designed to do two things: both gauge the constables' ability to recognize and accept a problem that has no real situations; AND their willingness to think outside of the box, and be able to adopt unorthodox solutions to those same unsolvable problems.
(If you want to get even deeper into the metaphysical nature of the Zeitgeist story, that what characters truly, deeply believe can change the world around them... it's a bit of lesson, that the unspoken rules you impose upon yourself will define your own limitations. If you allow yourself to be freed of artificial rules and limits, you can accomplish more than those who don't.)