A predator that evolves to run faster gains a real advantage against its prey — for exactly as long as the prey population hasn't also evolved to run faster in response. Once it does, the predator's improvement is effectively cancelled out, and both species are simply running faster than they were before, with the relative advantage back where it started. Coevolution describes exactly this kind of ongoing, reciprocal evolutionary response between two closely interacting species, and when that mutual response takes the specific shape of each side repeatedly evolving countermeasures to the other's improvements, biologists call it an evolutionary arms race.
Each side's improvement becomes the other side's new baseline
An evolutionary arms race unfolds because natural selection acts on each species independently, favouring whatever trait improves that species' own survival and reproduction in its current environment — and for a predator or parasite, "environment" includes the current capabilities of its prey or host, just as a prey species' environment includes the current capabilities of its predators. When one side evolves an improved trait — faster speed, better camouflage, a more potent toxin — that improvement temporarily shifts the balance in its favour, which in turn creates new selective pressure on the other species to evolve a countermeasure. Over many generations, this reciprocal pressure can drive both species' relevant traits to become considerably more extreme than either would likely have become facing a less demanding, unresponsive environment — not because either species is moving toward some fixed external goal, but because each is continuously adapting to a rival that keeps adapting right back.
The race can run for a very long time without a decisive winner
Because both sides in a coevolutionary arms race are typically capable of continuing to adapt, this kind of escalating interaction can, in principle, run for an extremely long evolutionary timescale without either species ever achieving a final, decisive advantage — a predator that becomes reliably too fast for its prey to escape would likely drive that prey population toward local extinction, removing its own food source in the process, which is one reason many well-documented arms races appear to settle into a persistent, roughly balanced escalation rather than one side simply eliminating the other outright. The "race" metaphor captures the ongoing, reciprocal nature of the dynamic well, but it can mislead if taken to imply a finish line either side is actually approaching; in a genuine long-running coevolutionary arms race, the relative balance between predator and prey, or parasite and host, is often what persists, even as the absolute level of each side's relevant traits keeps escalating over evolutionary time.
What we're still unsure about
The general dynamic of coevolutionary arms races, and numerous well-documented specific examples across predator-prey and parasite-host relationships, are well established in evolutionary biology, supported by both observed cases and genetic evidence of ongoing reciprocal adaptation. What's harder to establish with confidence for any given long-running arms race is exactly how it will resolve, or whether it will resolve at all, over a longer future timescale — since the outcome depends on future environmental changes, the appearance of new competing pressures, and the specific genetic variation each population happens to have available to draw on, all of which are difficult to predict with real confidence far into the future for any particular ongoing case.
This sits inside Coevolution & Evolutionary Arms Races, one of seven topics in Evolution, one of six domains in Biology, one of seventeen subjects the app can quiz you on.