What does C, W, Y and S Plans mean when talking about central heating controller?
The type of plan refers ultimately to the arrangement of the pipes and thus the type and number of valves you have in your system.

This page has explanations of all types (Y, S, W and G (not C)). Y Plan is based on a single three way valve that either allows the hot water from the boiler to the heating circuit, hot water circuit or both.

With S-Plan:


  ... you can have as many zones as you like, but each zone must have its own valve and thermostat. A popular way is to have 4 valves, 1 for the hot water, 1 for upstairs,1 for downstairs and 1 for say, the conservatory.


The W plan is an older control system.

The G plan is for gravity assisted systems. I couldn't find a "C" plan though.

I've also found this page which has diagrams of the Y-Plan and S-Plan controller circuits. They're quite technical so I'm reluctant to summarise here.