the anticipator in some (mainly older ones but can still get them now) works by: the neutral wire is heated when the stat is calling, and as it heats up, it allows the temperature sensor in the room stat (bimetallic switch usually) to heat up a bit quicker (usually 5-6 degrees or so). This means that the room stat reaches its set temperatue quicker, and breaks contacts (is satisfied) thus stopping the boiler heated water from going to the rads (until the temperature drops again and it makes, and thus puts power back on to the pump and boiler)!
the reason for an anticipator is: if the room temperature reached it's setting, ie 21 degrees c, the heat sensor (bi-metallic strip inside it) would then close (switch off boiler), but in doing so (over minutes) as it is slower to react, would then have reached over 21 degrees, thus meaning that the room was quite a bit over 21 and not very comfortable!! it basically allows the room temp setting to be shut off more precisely!!
a lot of room stats now, especially the digital types, use a thermistor inside instead, which is even more accurate and doesn't require a neutral wire either. some are battery powered or some just use the normal 2 wires (COMMON and CALL terminals)!-not sure how they get their power from though without the battery!...