Re: we were being held at the stop to help TFL synchronise the route.
The usual message is about evening out the gaps in the service.
The interesting one is (or used to be) Hyde Park Corner Eastbound on the Piccadilly Line, which had a thing called Balanced Headway. You'd frequently get a red signal there for quite a while and you'd get the occasional curious passenger asking the driver "why are we waiting here?" The answer was that "We're waiting for a train behind to 'drop on'." The idea was that the number of trains a certain distance behind that train must be greater than or equal to the number ahead of it in order for the train to proceed.
The shortcoming of the scheme was the limited visible counting 'horizon' the system had, it was all done using relays and long cables. With the advent of computer control it was possible to not only increase that horizon, but look at other factors too, such as trains approaching a converging junction in order to aggregate the timings.