I think the short short explanation is, speed wobbles is when the board can turn faster than you can react. When the board oscillates for whatever reason, it’s up to the rider to stabilize the board by giving opposite feedback.
To break it down into story mode:
A few things contribute to it, weight distribution being the most important. Keeping more than 50% of your weight over the front keeps the front end “steering” and the rear end “trailing”. If the rear end can turn more than the front, or if more weight is on the rear, the board will want to whip side to side, making it impossible to control. The same phenomenon can be seen in badly loaded auto trailers that are rear heavy, or driving a car in reverse where the “rear” end is steering. The actual physics behind this is complicated and can be explored further in trailer loading.
To assist in this, the rear trucks can have a lower steering degree - by lowering kingpin angle, or simply keeping the rear trucks tighter or fitted with firmer bushings will drastically help (but not a substitution for weight distribution. It is still critical to keep your weight forward.)
As speed increases, small steering inputs will cause more drastic movements, 2 things needs to happen now:
FIrst, finer control by the rider, aka learning the board and simply gaining experience. Nothing to do with the board here other than just riding, logging hours and slowly pushing to higher speeds until the rider gains better muscle memory.
Second, decreasing sensitivity via hardware. Extending wheelbase will increase the turning circle, which will slow down the rate of oscillation, making it easier to get under control at the same speed on a shorter board. Decreasing kingpin angle via various methods allows the rider to have more “leverage” over the truck hangers, both assisting in keeping them pointed straight, and also decreasing the sensitivity of input for the rider, allowing more margin for error before the board goes out of control.
In my opinion, increasing bushing hardness is not a permanent solution to removing speed wobbles. Bushings should be matched to the weight of the rider, allowing full cornering of the board without excessive pressure while giving proper feedback. Not enough and the board will tilt too easily, making it hard to feel for a center, too much and the board is sluggish, hard to turn and could possibly contribute to high speed wobbles.
Things that I believe has minimal effect on high speed wobbles:
Truck width (to an extent), longer is a bit more stable, short is more responsive, but it is more of a feel on how the board corners vs an actual factor to speed wobbles.
Board width, wider will give more leverage onto the kingpins, which should not make a difference with proper bushing hardness, but simply going wider may cause the board to have a wallowy feel simply because it is easier to leverage the kingpins without shifting weight as much.
Center of gravity, disagreeing with @annihil8ted, higher is more stable for skating. Lower is better for cars that does not involve balancing. Standing up with knees slightly bent is much easier than fully crouched on the board, think of trying to balance a pencil by keeping just one end on the tip of your finger. weight on top of the pencil makes it easy to do, a short and stubby pencil makes it much harder.
Weight of the board, usually irrelevant but a heavier board will be marginally more stable than an ultra light one, all other factors the same.