I wrote this summary of sail trim for another discussion but thought it might be useful here.
Amongst non- racing sailors, frequently there seems to be a misunderstanding of the term de-powering (reducing the power of the sails) resulting in the term being mistaken for shortening sail (reducing sail area by reefing or partially furling sails). De-powering a sail generally is easier and quicker than reefing, but still results in less weather helm and heeling while moving faster than a reefed sail would permit.
In a general sense, there are a lot of factors in powering up or down a sail but the two biggies are the depth of its camber and the angle of attack. The deeper the camber (curvature of the sail) the more drive the sail develops, but along with drive (which is the forward component of the force generated) with increased camber comes a higher side force as well. This side force causes heeling and leeway. In really light air, the airflow lacks sufficient energy to flow around a sail with too deep a camber so the sail may actually be slightly flattened. As the wind picks up, you can introduce deeper camber which is how you 'power up' a sail. Powering up involves and easing of halyards, outhauls, and backstays.
As the wind builds, so does drive but at some point hydrodynamic drag becomes the limit on speed, and at this point additional drive is not necessary. As this point is approached, heeling and weather helm become excessive. As the boat approaches this point, the sails need to be de-powered. To begin to de-power the sails, halyards, outhauls, and backstays are tightened. This pulls fabric out of the body of the sail, flattening the sail. The sail produces less forward drive, but it also produces less side force.
The second aspect of this discussion is angle of attack (the angle between the direction that the wind hits the sail and the sail itself). For any given wind and sail shape, at any point on the sail, there is an ideal angle of attack. If the angle of attack is too flat, the sail luffs, and if the angle of attack is slightly too steep, the sail generates less lift and more drag and greater side forces causing more heeling and leeway. In the extreme case of too steep an angle of attach, the airflow stalls and very little drive is generated, and side forces go up dramatically.
Because of gradient wind effect, (air moving slower near the water than higher in the air due to the friction between the water surface and the air above) in light air, the apparent wind angle felt by the sail will be different at the head of the sail than at the foot. The apparent wind at the foot of the sail will appear to be more forward than the air at the masthead. To allow the sail to have a proper angle of attack twist is introduced into the sail so that the upper part of the sail has a different angle of attack than the bottom of the sail. Here is where the traveler, backstay, and the boom vang come into play.
By bringing the traveler to windward, the pull of the mainsheet becomes more horizontal than vertical. In doing so, the boom is held inward toward the centerline, but the boom is allowed to lift a little, and that lifting eases the tension on the leech of the sail allowing more twist to develop.
As the wind builds, gradient effect generally becomes insignificant, so the whole leading edge of the sail wants the same angle of attack and in general, that angle of attack needs to be much flatter than it would be in moderate winds. To unify the angle of attack, the traveler is lowered to leeward and the mainsheet tightened, which increases the downward force on the leech of the sail. This increased leech tension removes the twist from the sail. As the wind builds the angle of attack can further be lessened by lowering traveler further to leeward. As you bear off on a reach, the traveler can be further lowered to maintain the proper angle of attack without powering up the sail, but at some point the sail needs to be eased broader off than the length of the traveler can permit while still generating the proper downward force, at that point the Vang takes over the main role in controlling twist and the sheet then simply controls the overall angle of attack of the sail.
Simply easing the mainsheet in a strong breeze does allow the head of the sail to twist off and reduce heel, but it comes at a price. In easing the sheet the boom rises and allows more fabric into the body of the sail increasing power just when you need to reduce power, and also in order to obtain enough drive, the lower portion of the sail is over trimmed developing a lot more weather helm than would occur with proper sail bladed out sail trim.
The backstay tension (especially on a fractional rig) can be used to de-power the rig further. On any rig, even one with a stiff mast, tensioning the backstay removes sag from the forestay and is doing so, draws fabric out of the sail in a horizontal direction, flattening the jib and de-powering it. As the forestay is tightened the mast moves aft and that also changes the relationship between the jibsheet lead and the head of the sail, allowing the leech of the jib to open slightly, reducing the angle of attack of the upper portion of the sail. On a boat with a bendy rig, and more dramatically and controllably on a fractionally rigged boat, as backstay tension increases the mast bows forward, in doing so it also draws fabric out of the sail de-powering the sail in the same manner that tightening the forestay flattens and de-powers the jib. Also similar to the jib, the masthead moves aft as the backstay is tightened and that opens the leech slightly at the head of the sail, easing the angle of attack and further reducing heeling, weather helm and leeway.
There is a tendency to dismiss this as 'racer stuff' but these kinds of subtle sail trim adjustments can make for a much more comfortable and controllable passage as well as adding significantly to the speed of the boat.
Lastly, really disagree with the idea that "if your sails are basically trimmed correctly, and you are making the kind of fine adjustments that a skilled racer would use, those fine adjustments can't be measured by your knotmeter". Small adjustments to backstay or traveler positions can tremendously reduce weather helm and heel angles. On my prior 28 footer, these fine tuning items were good for a half-knot or more, and on bigger boats or in higher winds, these kinds of minor adjustments can yield enormous gains in speed and comfort.