From Roader's Digest: The SABRE Wiki
A Green Wave is a facility in UTC that is used to clear a route of traffic to allow easier progression for emergency vehicles. It is also a term universally - yet somewhat erroneously - applied to the practice of keeping a platoon of traffic moving through successive junctions. The correct term for this latter practice is Green Progression. Green wave - Grüne Welle - is the actual term used in Germany for Green Progression. 
Since the early days of traffic signal engineering, it has been usual practice to ensure as far as possible that traffic can get through successive junctions without having to stop. Due to the explosion in car ownership, in the 1970's TRRL devloped a computer program called TRANSYT, which calculated the most efficient timings for networks of traffic signals.
For arterial routes, this program allowed traffic signal junctions to be better co-ordinated, especially as at the time, fixed time plans were the norm for these types of junction during the day.
Most drivers will see green progression on a small scale, for example, at a signalised roundabout or road with a series of signalised junctions. There are a number of ways a highway authority has of ensuring co-ordination between junctions;
Fixed Time Plans or Cableless Linking Facility Plans
These are timings of fixed duration and as the term suggests are based on calculated green times for a specific volume of traffic. This type of plan is very inflexible and is usually determined by time of day rather than actual traffic flows. The offsets between each junction are calculated to ensure that traffic is able to progress between each junction in the most efficient manner.
SCOOT is the next step from the original TRANSYT program, calculating the optimum green times in real-time and adjusting green times at each junction to be the most efficient for the network.
What is Progression?
Imagine a queue of traffic at the first junction in a line of junctions; when this platoon of traffic sets off towards the next junction there will already be a few vehicles waiting at the next stop line along. SCOOT will know roughly how much traffic is heading to this second stop line as well as how much is already waiting. When SCOOT changes the second stop line to green, the platoon make up will have changed such that those at the front of the first platoon are now in the middle of the second platoon.
As is the way with traffic platoons, the rear of the platoon will gap out more than the middle, thus it is not efficient to keep the traffic stage at green to the detriment of other traffic flows. Thus it is likely that those at the rear of the first platoon will be "cut off" to form the front of the next platoon.
This sequence will continue right through the junctions so that the main bulk of the moving platoon will get through. This does not mean that the car who was at the front of the queue at the first stop line will always get all the way through to the last junction. It is always in the Engineers interests to get the maximum number of vehicles through the network as efficiently as possible.
In tidal situations, the Engineer will generally use different timing sets for to bias the inbound and outbound flows as appropriate. SCOOT will work in a similar way, using its default model to decide the best green times and generally adapting quite well. It is common for traffic engineers to apply offset weightings to links that form the inbound and outbound routes at different times of the day, to influence how SCOOT responds to changing flows.