Let me give a bit of context which makes it easier to understands this funny language.
The number of landings that an airport can handle in an hour depends on a number of factors. One of these factors is the weather, others are for example the staffing of the Air Traffic Control unit, the availability of runways (e.g. maintainance) etc)
When more aircraft fly to an airport than can be handled, Air Traffic Control will start to put aircraft into a holding. This is a place where aircraft fly circles to wait until it is their turn to land. If there are more planes arriving than can be handled for a long time, the number of aircraft in the holding increases, and the time than they have to fly circles does increase as well. This is inefficient because it costs a lot of fuel, it can become critical when they have to stay there so long that they start to run out of fuel, and if the airport suddenly needs to close down for whatever reason all these aircraft need to divert to other airports causing chaos/unsafe situations, especially when there are many of them.
In order to prevent these situations, Air Traffic Control assesses the situation regularly and makes an estimate of how many planes can be handled in the next couple of hours. Combined with the number of aircraft already holding to wait for their turn to land, ATC declares a capacity. This capacity is then sent to the Central Flow Management Unit in Brussels. CFMU then puts a so called Regulation into their system. In your example this is LLTCWX capaticity, meaning that London Heathrow Terminal Control has a capacity of only X aircraft per hour for weather reasons.
CFMU is also the unit that processes all European flightplans, so they know who is planning to fly to London Heathrow. They will count all the flights going to London and when they see that the number of aircraft are planning to fly to Heathrow exceeds the declared capacity, they start to issue slot delays to individual flights. This could for example mean that the flight from Frankfurt is told not to depart on its planned time, but wait for another 30 minutes. Unfortunately for the passengers they are now sitting in the aircraft on the ground and have to wait for 30 minutes, but it is better than flying circles for 30 minutes.