Imagine a locomotive pulling a boxcar on a parallel train track with a chain. The tension in the chain is higher due to the sideways component of pull, but the work done in moving the boxcar is exactly the same as if the locomotive was directly in front of the boxcar requiring a much lower chain tension.
The increased tension in the chain when pulling from the side is analogous to the increased current necessary to supply the reactive power in an electrical circuit. The chain has a limited capacity for tension before it will break, just as electrical wires have a limited capacity to carry current before failing. By increasing power factor (putting the locomotive in front of the boxcar) capacity is freed up in the electrical system (the chain has more spare tension before reaching the breaking point).
