The reason that the red queen principle exists is that evolution
carries on happening. One problem that was found with mathematical models
of evolution was that populations tended to reach a point and go no further. Despite the tenent that fitness
is maximised within a population (which turns out to not be true, but that's another issue entirely), it wasn't happening.
Eventually, somebody twigged. Selection is generally due to competition against othe members of the same ecosystem. If we hypothosise a species of bird that carries a parasite that has a harmful effect on the carrier, it's obvious that selection will favour those birds who are best able to resist the parasite. Over time, the fitness of the population of birds will increase until it reaches a new equilibrium point.
Now for the obvious flaw. The birds are evolving to resist the parasite, thereby increasing the selection pressure against the parasite. In order to survive, the parasite must itself evolve. This in turn favours further evolution of the bird population to resist the new, better parasite. The two populations therefore continue evolving purely so that they can maintain the same relative fitness. A common analogy is to liken it to a nuclear arms race - as each participant comes up with a new weapon, the other participant is forced to come up with its own defence against it. Given long enough, its possible that the birds will develop sufficient intelligence to wipe out the parasites once and for all - it's also possible that the parasites will gain enough intelligence to start farming the birds. At that point things start going funny and natural selection becomes less important.
Thankfully for evolutionary biologists, only one species on the planet seems to have got to this stage and therefore it can be written off as a special case.