Edge grip is exactly what it says: the amount of grip that the edge of a ski had on the snow. More edge grip can be achieved with sharper edges. A ski with more edge grip makes it more difficult to slide sideways when the ski is on its edge (i.e. not flat on the snow). Edge grip is more important on hard snow than in soft snow. In soft snow, when the skis sink a little bit into the snow, maintaining a certain line is not very difficult. The resistance of the snow prevents you from sideslipping. On hard snow, it’s all about good edge grip.
Torsional stiffness is the ability of a ski to withstand torsional movement. When you tip a ski on its edge, a torsional stiff ski will transfer all that movement to the edge and onto the snow. In a ski that has less torsional stiffness, part of that effort is lost in the ski. The extremes of the ski twist less than the point under the binding. Torsional stiff skis have more directness and edge grip, but also punish you more if you make unintentional movements.
A carved turn is a turn in which every part of the ski’s edge goes through the exact same arc. There is no sideslipping in a carved turn. Carved turns are fast because they cause less resistance between the skis and the snow. They are made by putting the ski on edge, bending the ski, and having the sidecut of the ski literally carve through the snow.
Skidded turns are turns that have sideslipping in them. Most lazy turns are skidded. It is not better or worse than a carved turn, just different. Since there is more resistance in a skidded turn than in a carved turn, skidded turns are mostly used to get or gain control over one’s speed. A skidded turn that becomes a carved turn is called a ‘slarved’ turn.
Float means the ability of a ski to stay above the snow. Mostly, this refers to the tips not punching under soft snow. Float is achieved by the shape and (rocker) profile of the ski, and the total surface area. Wider skis have more float than narrow skis.
Rebound is the energy that the ski ‘gives back’ at the end of a turn. While skiing, you bend the ski and put in energy (mostly through your mass and centrifugal force). When, at the end of one turn, the ski releases that energy you put in and it pops back to its unbent state, that energy return is called rebound. It helps release the old pressured ski and the transition of weight onto the other ski. Typically, skis with more camber underfoot have a more natural tendency to have a good rebound than skis with less or no camber.
Damping is the amount of vibration that is filtered out by the ski before they reach your foot and a ski feels bouncy. Different materials are used to absorb vibrations. Titanal does that, but also rubber, fiberglass, basalt, other synthetic – mostly stretchy – materials. Some brands add a ‘dampening system’ with other means of vibration absorption (any other way of vibration dissipation). They use those to market their products with a unique selling point.
Pop is a release of energy in the ski, just like rebound. Other than just rebound, it seems to add some extra explosive energy, making the ski almost ‘jump’ off the snow. It is a lively characteristic that carbon tends to have. The downside of a ‘poppy’ ski is that in most cases, dampening properties are not great. You can have a ‘rattle’ ski on hard snow.