From a FOC (freight operating company) perspective, control is an office-based role concerned with the real-time management of services 24 hours a day on a shift basis.
The planning side of the FOC (generally a 9-5 job) will have a weekly plan in place where schedules (STP or WTT) have been arranged with Network Rail, traincrew have been rostered and loco diagrams created to cover a specific set of services. Train Running Control will monitor these services and when things happen that disrupt the plan, the general idea is manage things "back to the plan" as smoothly as possible.
The control job can involve a lot of telephone calls. Some of these will be answering questions, or contacting yards / drivers / groundstaff / customers / Network Rail to make sure they are aware of anything happening which deviates from the plan. The main function of the control job could be summed up as dealing with problems that arise when running trains, making decisions to resolve them, and co-ordinating the response. As per post #8, if everything ran completely smoothly, no delays, no incidents, no train / infrastructure or equipment failures of any kind, no staff sickness, everything running exactly to plan and on time, in theory control would be sat around monitoring things and drinking tea without needing to intervene.
In the FOCs I think safety-related incidents are generally dealt with separately from train running, through a "duty manager" (effectively a senior controller in overall charge), a role which requires additional training on safety rules. Depending on the size of the company, loco control is also likely to be a separate function. The loco controllers allocate specific engines to the loco diagrams put together by the planners. They arrange loco swaps as required to position locos for planned maintenance, find locos to replace any that fail, make sure locos are fuelled and serviced as necessary, organise any short-notice loco movements or swaps that are needed due to specials, cancellations, delays and so on. The overall aim for loco control is to ensure there is a loco in the right place at the right time to work the trains that are planned to run, and that locos reach depots on time for planned maintenance.
Maintenance control may be a separate function - these controllers are usually people with experience of maintaining engines and will answer calls from drivers who have a loco fault to find the cause and determine if it can be resolved easily or if the train will need rescuing. I assume the TOCs would have a similar role for dealing with unit issues and helping drivers diagnose and hopefully resolve faults.
As an example of a incident, if a loco hauling a freight train fails and blocks the main line, and maintenance control determine the train needs assistance, the loco controller would need to identify a suitable loco to rescue it, and the train running controller would find a driver for that rescue loco. In some cases another haulier might provide a rescue engine, co-ordinated through Network Rail. The end customer for the train would need to be informed about the potential delay or cancellation. The FOC controllers (or duty manager) would liaise with Network Rail control to manage the incident, for example to let them know the origin and work out the ETA of the rescue loco and discuss if the train will be assisted from the front or rear and so on.
During the same incident, Network Rail control (which I think is generally divided into route control for general train running plus a separate incident control) would then also be speaking with the TOC controls to manage passenger services that might be disrupted. Controllers at the TOCs will be monitoring the situation which may be causing them delays or require cancellations of their services, and be looking at the positioning of trainsets and traincrew of delayed or cancelled workings and so on, with the same general idea of managing things "back to the plan." This might involve the kind of alterations (terminating short or skipping stops) mentioned in the original post.
Controllers across the TOCs, FOCs and Network Rail will all be dealing with the effects of disruptions that have a general impact on the network, things like fatalities, cable theft, train failures on the main line, infrastructure failures, short notice emergency possessions required to fix those infrastructure faults, severe weather and so on. Network Rail have an overall network management role where they can make decisions to hold freight services back during disruption (prevent departure from a terminal or hold a train in a goods loop for example) to avoid having too many trains stood on the main line with nowhere to go. One problem with severe disruption is that it can quickly overwhelm the capacity of control teams to deal effectively with it - the workload on a control job can vary enormously depending on the situation.
Train running controllers may also be dealing with problems like finding cover for drivers that have gone sick at short notice, or finding cover for any traincrew vacancies that couldn't be filled during the normal planning / rostering process (I think TOCs would be more likely to have some kind of dedicated train crew management within their control function). Delayed trains can also result in the need to find additional traincrew due to a driver being "out of hours." Ideally these issues can be managed behind the scenes without causing delays or cancelling services. Freight trains can have issues that don't affect passenger services, such as the breakdown of terminal equipment causing delays with loading or unloading, and part of the job will involve communicating with customers (the larger FOC controls often have train running control split up by commodity or customer rather than area).
As an example of controllers managing freight services back to the plan, if an intermodal train was heavily delayed into a terminal or port due to network disruption, in consultation with the customer they may decide to "strip" the train without reloading it, or only load priority traffic, to turn it around more quickly and avoid a situation where a train arrives very late, departs equally late and can't realistically be recovered back to right time running due to tight turnarounds and limited recovery time in the schedules. The same may apply to other trains, where a decision needs to be made whether to send a train back without being fully loaded / offloaded to limit delays and get services back on time. Another example - if a freight train gets cancelled after being loaded (e.g. due to network disruption preventing it reaching its destination) it becomes a "stood load." Control might be involved in organising a special to get the train to its destination (finding a loco and driver and arranging a VSTP schedule through Network Rail), or depending how urgent the traffic is, in some cases it may be more realistic to pick up the next planned working the following day.
While control is an office-based function (traditionally a control office, although FOC controls may actually be in the same office as their planners and other 9 to 5 staff), there will also be managers based "in the field" that actually go out and help deal with various kinds of incidents. I think Network Rail have "Mobile Operations Managers" (MOMs) while the FOCs will have area managers or similar "on call" staff to go out and deal with incidents and other problems that need a management presence.
Obviously roles and responsibilities will vary from one FOC to another, with some roles being combined in smaller companies, but that's a simplified general overview of control from the freight side of things.
For some pages of traditional control logs from the 1970s BR era on the Western Region, see this flickr album from rivercider:
https://www.flickr.com/photos/rivercider/albums/72157632247621916/
The trains have changed, the organisations and jobs have changed, but it gives a flavour of what control work as a whole is about, from dealing with train or infrastructure faults and staffing issues, to random incidents like "Driver of 1330 Paddn reports at 1502 naked man on line at Lavington."
