ToME: the Tales of Maj'Eyal

What exactly does global speed do? Does increasing it increase both attack speed and movement speed?

Yes. It also increases the speed of effects/cooldowns/etc of the player since all of those are relative to the actor they are on. For example, if you are poisoned and then increase your speed to 200% the poison will still hurt you every chance you have to act. This can be very important for talents such as Lightning Speed, where your global speed is really cranked up but if you do anything but move (so use a talent/infusion to remove the poison) you break the effect.

...which means that lightning speed is potentially quite useful as a cooldown and effect-purging skill. Fascinating.