Well speed bonus is a % increase or decrease of your damage that depends on your and your opponents movement relative to the strike. For the example, let's say we have a dude who does consistently 100 damage (so it is easy to calculate).
If he stands still and his opponent stand still and they both face each other squarely, then there will be a speed bonus of 0% and he will do 100 damage, no matter the attack direction.
If he is standing still and the opponent is running towards him and he does a stab he gets a high speed bonus. Let's say +50% speed bonus. He will then do 150 damage to the opponent.
If the opponent is standing still and he is running forward he will get the same bonus (if they run at the same speed of course. Someone walking will give less speed bonus than someone running), which is +50% and he will again do 150 damage with the stab.
If they both are running towards each other then both their speeds are added to the equation and he gets a speed bonus of +100% and will do 200 damage.
Now speed bonus also works on the sideswings but a bit different. If the opponent runs towards him and he does a left swing then he will get a speed bonus but it will be less than for a stab. This is because the stab is in the direction they are moving towards each other, while the left sideswing is a left to right direction. Thus it will be normally lower, for example +25%, and the damage would be 125.
But if the opponent was coming from the right, running right past him, and he did a left sideswing, than that would again give him a boost, I would guess somewhere around 50-70%. Not quite sure here with the numbers but somewhere around there I believe.
Now what if the opponent is backpedaling while our guy stands still. The speed bonus would then be
away from our guy and go into the negative. Since backpedaling is slower than running it would be around -25% damage and he would do a total of 75 damage.
Now if the opponent is facing away and running (a -50% since he is at full speed) AND you are backpedaling (since away from him -25%) you would get a speed bonus of -75% and do a total of 25 damage. This way you can also use speed bonus defensively, reducing the damage you take. Also speed bonus comes before the armour reduces (it affects the raw damage of the attack) so if you reduce the damage and have high armour, you can easily negate all of the damage.
Also if you are running towards him and he is running away, the relative speed between you will be 0 and you will get a 0% speed bonus, doing 100 damage.
Looking back this might be a bit confusing so just to make the main point again. Sooo,
TL;DR: If they move INTO your attack then you do more damage and if you run the way you are attacking you also do more damage. If he runs AWAY from your attack then you do less damage and if you run opposite of the direction you are attacking.
Also all the numbers are just random. I doubt they are EXACTLY those speed bonuses, but the relation between them (like two running towards each other is double of one running towards a standing) I believe is right. I think the actual speed bonuses are much higher, a charging horse with normal speed have about +200% speed bonus, at least in SP. This is why they do so much damage, although it works both ways.
If someone have the actual numbers then please come with them, I would love to see them too.
Also there are other factors that change the damage. Like when in the animation you hit, how long the attack is held, where you hit, armour, damage type etc. If you want to understand speed bonus more I suggest you go play Single Player. Whenever you hit someone you will see how much damage you did and the speed bonus for it. That's how I learned how to move to get the most out of my attacks. Although I still suck at blocking
