How does the blade move or slide over the ice?
If you apply pressure to ice, it melts. When the blade presses against the ice, it creates a thin film of water, which acts as lubricant to allow the blade to slide. When you are skating, you actually are skating on a thin film of water.

Why does the blade turn when I lean?
Next time you skate, glide straight ahead on the blade. Using your ankle and nothing else, tilt the skate to the right or left, and feel how it turns you in that direction. View the blade from the side and notice how it curves up at the front and back (it has "rocker"). Pressed into the ice, a short length of it is actually in contact with the ice. As it is tilted onto an edge, you can probably envision that this length of contact is slightly curved. As the blade moves along the ice, it will follow this curve. The curve will be deeper if you lean your ankle more. It will also be deeper if your blade has more of a rocker, as most blades are toward the front. As you glide on an edge, press slightly forward on it, and feel how it tries to curve more.

What is the hollow?
You probably know that your blade has two edges, inside and outside, and that there is a "hollow" between the edges. You may also know that the hollow can be "deep" or "shallow", and be able to feel the difference by running your finger across the blade. Refer to the following figure showing a cross section of a blade. The blade is made of a piece of steel of some thickness (a typical freestyle blade is about 0.15" thick). The bottom of the edge is ground out with a circular cross-section (see "how is a blade sharpened", below). The radius of the circle is called the Radius of Hollow (ROH). The shorter the ROH, the "deeper" the hollow. A blade with a deep hollow will hold the ice better, but will also be grabbier and slower.

What is the correct hollow for me?
This is a very individual matter. I will state some facts, and then some opinions. An important thing to note is that the ROH (see question "What is the hollow") does not tell the whole story about how a blade feels. The blade touches the ice only along the edges, so what's really important is the angle between the side of the blade and the bottom of the blade at the edge. Some blades are wider than others. For example an MK Phantom is 0.155" wide, an MK Dance is only 0.11" wide. If you have a geometric mind, you can probably see that, given the same ROH on the two blades, the wider blade will have a sharper angle at the edge. So, to give the same strength of edge, narrower blades will need a shorter ROH. A more acute edge angle (deeper hollow) makes the blade less likely to slide sideways, so a deeper hollow gives more secure edges. There is more to it than that, though. It also makes the blade more determined at going where IT wants to go, so it will be harder to control (more likely to grab or "catch an edge"). And, the deeper cut into the ice causes more drag, so the blade will be slower. Given these tradeoffs, one could state that the optimum ROH is one which is just deep enough to give the skater the required edge security. Learning proper use of the ankle to control edges is important, and a shallower hollow facilitates this. As the skater becomes more advanced, they are likely to use a deeper hollow to gain security of the edge. This may be especially important to advanced freestylers desiring edge confidence on jump takeoffs and landings. On freestyle blades, I see ROHs varying from 7/16" to 5/8". The following graph shows bite angle versus ROH for various blade widths (The MK Dance is 0.11" wide, Wilson Dance is 0.14" wide, most skates are 0.15" wide, Phantoms are 0.155" wide at their widest part). Given a desired bite angle and the width of your blade, you can look up the radius of hollow required to give that bite angle. A 10-degree bite angle is pretty deep, and a 7-degree is fairly shallow.

What is the rocker?
If you look at the blade from the side, you will see that it curves from front to back. This is the rocker. Blade companies generally specify the "rocker radius" for their different blades. If you draw a circle of this radius (typically 7 or 8 feet), approximately the back 2/3 of the blade will have a fairly circular contour that matches the arc of the circle with a 7 or 8-foot radius. The radius of curvature decreases toward the front (there is more curve), giving the blade a complex shape. The increased curve toward the front of the blade has an interesting effect. If you move your weight forward on the blade while on an edge, it will want to turn on a deeper edge. You may know that you spin on this part of the blade. You probably have also felt how the blade can grab if you rock back on it while spinning. A long radius of curvature gives a faster, more stable blade. This is why speed skates have very little rocker. It also gives less maneuverability, which is a reason why figure skates curve more at the front. MK blades are mostly specified to have a 7-foot radius and John Wilson blades have an 8 radius specification. A recent check of many new blades indicated that the MK blades were pretty close to their specified 7-foot radius, while Wilson blades were closer to 6. Of more concern is the considerable deviation that is seen, in the form of local "humps" in the rockers at various points on the blade, of both brands. Their specified radius is not precisely controlled. A good sharpener can detect these humps and usually correct the rocker. Of course, it is also quite possible that careless sharpening can introduce such problems as well.