Synergy is a brand name used by BT to market these phones. There are a range of different models, so the features vary according to the model.
But common to all of them is the ability to take the phone anywhere around the house and garden, and to have several of them located around the house, but only the 'master' phone needing to be actually connected to a phone line.
I have a trio of model 4500, and they are fine. BT don't actually make them - they come from China. Argos is one place to buy them reasonably competitively, with a no quibble return policy if you don't like.