Edge control is not just the ability to do some fancy stops. It is the beginning, middle, and end of all skating on flat ground.
The designers of the wheels and bearings and other rolling components on your rollerskates went to great effort to reduce the rolling resistance of those components. Lubrications have been developed to reduce friction in the bearings. Materials have been designed to reduce hysteresis in the wheel itself. Ounces have been shaved, and forms have been tested, and as a result your wheels roll very well along one axis, and one axis only. They roll forward and backward.
This is the least interesting thing about them. Set someone rolling forward, and they will continue to roll forward until those tiny friction forces that the rollerskate designers could not entirely eradicate slowly bleed away that initial energy input. Then they stop.
For anything interesting to happen on rollerskates, the skater must push through the edges of the wheel. Change requires resistance. Examples below.
E1. A skater rolling in a straight line on a level floor pushes out and back in order to maintain speed. If you look at the positioning of the skate and the resulting motion of these pushes, you will see that the input forces operate through the edge of the skate wheel. The skater turns their feet slightly outward, and then pushes off slightly inward with every stride. The skater never pushes along the axis of roll, because no force can be supported along that axis.
E2. A skater rolling in a straight line on a level floor leans heavily to the left, causing the trucks to compress on the left side of both skates. This turns the wheels slightly left of the direction of roll, which means the right edge of the wheels is being pushed against the friction forces of floor. If the leftward reaction force of the floor on the skater does not exceed the static friction limit of the wheel/floor interface, the skater will turn left. This is called carving.
E3. Combining the concepts from E1 and E2 produces the cornering technique known as “crossovers.” Every stride in a crossover is also a carve.
E4. A skater rolling in a straight line on a level floor turns both their skates 90 degrees left or right of the direction of roll, and rapidly stops. This is called a hockey stop. In a hockey stop the inside edges of one skate and the outside edges of the other skate both work together to reduce the skater’s momentum to zero.
E5. Point the toes towards each other while rolling forward and dig with the outside edges of both skates for a plow stop.
E6. If one of the skates is allowed to roll instead of turned sideways, it is a half plow.
E7. Point the toes away from eachother while rolling backward, thus engaging the outside edges of the wheels, and it is a reverse plow.
E7. Drag the inside edges of the wheels of one skate behind you, and you are doing a T-stop.
Many other slides and stops are possible once edge control is understood. Start by noticing and appreciating how the edges of your wheels control all momentum transfer that does not rely on toe-stops. Feel the wheel edges bite the floor in each of your crossovers, in your carving, in your stride. Feel the way that edge resistance connects you to the floor and the Earth below, transferring energy and information along a friction interface. Then, when you feel you understand the connection, move on to learning stops and slides by rapidly and aggressively engaging those edges.
Flatground energy transfer requires resistance, and resistance requires using the edges of your wheels. Nothing changes without resistance, and with it, everything eventually becomes heat. Every push and slide and crossover you do brings the heat death of the universe infinitesimally closer. As does your every step, breath, and thought. Use them all wisely.