Impulsion is a tricky thing, because while we often understand what someone means when they say impulsion riding-wise, we may not understand where it comes from or how to improve it. Impulsion is the amount of power a horse can put into his stride. Notice that I say power, but not a direction. That is because there are two different types of impulsion: longitudinal (forward) and latitudinal (up/down). Impulsion itself stems from the fact that horses have no muscles below their knees/hocks. There are only tendons that move the lower limbs. In order to carry out a gait, these tendons are stretched or loaded like a rubber band, then they snap back to their original size when released, flinging the leg backwards and propelling the horse forwards. More impulsion comes from increased loading of these tendons, as it is like stretching a rubber band - the more you stretch it, the harder and faster it snaps back. These tendons can be loaded in two ways, as mentioned above.
The first way is the more basic of the two, longitudinal loading. You can see Sid exhibiting excellent longitudinal loading above. In this sort, the horse reaches far beneath him with his hind legs, which creates leverage on the tendons and stretches them. As you can see, this loading would send the horse forward when the horse passes over the leg and the tendons are released. This is why "tracking up" an a full stride length is so important to many trainers, and why true extension is shockingly difficult to achieve.
The second way of loading the tendons is latitudinally. You can see the brown horse above executing latitudinal loading. In this, the horse brings his weight over the hind legs, pressing the ankle straight down and allowing his weight to load the tendons. This sort of loading would send the body upwards, rather than forwards, because the body does not have to travel as far for the tendons to release. This is true collection, and this free loading is why it is so difficult to achieve full collection.
Feel free to ask any questions you have below!