Yielding to pressure is the single most fundamental principle in horse training — the idea that a horse learns to move away from, soften toward, or otherwise respond to a physical or spatial cue by discovering that doing so produces the release of that cue. Every trained response a horse has, from leading on a halter to executing a flying change, is built on this principle. The horse does not comply because it understands our language or because it wants to please us in an abstract sense — it complies because it has learned through repetition that a specific response to a specific pressure reliably produces the relief of that pressure.
The pressure itself can take many forms: the feel of a halter against the poll, the squeeze of a leg against the barrel, the weight of a bit in the mouth, the tap of a dressage whip on the hindquarters, or even the spatial pressure of a handler's directed body energy. What all of these have in common is that they are applied with an intent to produce a response, and they are removed the instant the desired response occurs. The removal — the release — is what the horse is actually learning from. Without the release, there is no learning, only increasing pressure that the horse eventually learns to brace against rather than yield to.
Understanding this principle changes everything about how a trainer communicates with a horse. The question shifts from how do I make this horse do what I want to how do I apply pressure clearly enough that the horse can find the release, and how do I time the release precisely enough that the horse connects it to the correct response. Answering those two questions well is the entire art of yielding-to-pressure training.