Across the skiing community the basic fin tuning rules of thumb have been reiterated a million times, but I have heard very little talk about why these adjustments do what they do. Since we do not have telemetry or empirical data to prove or disprove these theories, they are just theories.
Your ski is a Lever on a sort of teeter totter that pivots somewhere around the middle of your back foot. All turning activities center around how you manipulate your ski in relation to the fulcrum or pivot point of this teeter totter. Some skiers stay on the front of the lever and keep the tip of the ski down though the turn, some ride the back of the lever, and a third group shifts and changes the lever's attitude though the turn. Fin blade settings control the back of the lever and you control the front.
Blade length (Also known as Tip Pressure): It has been experienced by most skiers that when length is increased the attitude of the ski flattens as the ski coasts out to the ball line on his (or her) so called Off Side(a.k.a. Bad Side or Toe Side). Simply put, for a Right Foot Forward skier, the nose height of the ski in the pre-turn on the 1/3/5 side of the course is affected by blade length. The question remains: why does a longer blade affect the skis attitude on a specific side of the course but not the other and to go a step farther, how does the length of the blade change the attitude of the ski.
On the Off Side it is more natural for the skier to place more weight on his front foot which sets the attitude flatter. With the Teeter Totter already leaning forward the ski is more susceptible to additional changes in forward attitude. As the blade gets longer it creates more drag. Drag from the back end of the lever pulls the whole ski deeper and flatter in the water. On a skiers so called On Side (a.k.a. Heel Side) his stance is naturally a little farther back so the Teeter Totter is weighted to the back and is less susceptible to the variation of drag caused by changes in blade length. A trend with a lot of skiers today is to run a blade with less length to allow the skier to more manually adjust the ski attitude on his Off Side.
Perhaps the most finely tuned and most sensitive of the settings is depth. Depth controls the amount of water pressure that is exerted on the lever (ski) though the turn. Without enough depth the front of the lever (the skier) will over power the back and the tail of your ski will slide out of control. In this case, the skiers inertia is pushing on the back of the ski and the fin blade does not have enough surface area in the water for the tail to hold its ground. The blade needs enough water pressure to control its end of the lever.
With too much depth, something somewhat surprising happens. As described above when there is not enough blade in the water the tail slides but when there is too much blade this creates excess pressure that has to be relieved. This excess pressure lifts the whole ski out of the water creating what is known as tip rise or Wheelie. With too much grip on the water, the blade overpowers even the strongest skiers.
Front to Back: The Front to Back adjustment is said to be the least sensitive, and I believe that it is the most misunderstood movement. Moving your blade backwards and forwards simply changes amount of lever behind the fulcrum. As the length of the lever behind the fulcrum changes, a number of aspects of your ski's performance also changes. Just as blade length changes the attitude of ski in the water on your Off Side, the Front to Back adjustment does the same thing for your On Side (Heel Side). As the blade is moved further back on the ski and the lever is elongated, the tail of the ski gains leverage over the front of the ski. As this leverage is increased, the attitude of the ski in the pre-turn is flattened. When the blade moves further from the pivot point it is as if you are riding bigger ski or at least one with a bigger tail.
When the blade is moved forward, the tip of the ski comes up on the On Side. As fin leverage is decreased your ability to manually control ski attitude increases. Because most skiers have more weight on their back foot on their On Side this release of leverage brings the nose of the ski up. You have more control of the skis attitude with the blade forward, but it is often easier to trim the tip height correctly and not have to adjust it manually at the ball by moving your weight around on the ski.
The second effect of this adjustable length lever is the size of your turn radius on both sides of the course changes as the amount of lever behind the fulcrum changes. As the trailing half of the lever gets shorter it is easier for the skier it manipulate the ski to turn harder and faster. With the blade farther back, the ski will not only carve a smother and wider arc but for some skiers this will result in greater angle. As with above, this change has a similar feel to changing ski size.
Lastly on the subject of Front to Back: Once you see that this adjustment is a change in lever length, then it starts making more sense to move your bindings and fin at the same time. In an attempt to get a better wake crossing some skiers will move their bindings back but will forget that not only are they changing the balance point of the ski (fulcrum) but also changing the length of back end of the lever. If you are considering moving your bindings back, you might also consider moving your blade back. Of course you may benefit form one of the adjustments and not the other.
I hope this helps you understand a little more about the basic blade adjustments. There are, of course, many more implications to each movement than what is listed here and with each adjustment there is a trade off of some sort. When you understand your lever, it is a lot easier to make it do what you want it to do.
Note: For simplicity I have used the terms On Side or Good Side and Off Side or Bad Side because of their acceptance across skiing. As a Right Foot Forward skier, I have a much better 1/3/5 side. So I guess I have a good Bad Side and a really bad On Side!?!?!?! I really object to these terms and wish we all used Toe Side and Heel Side.