Social dance is similar to barn dancing, or country dancing. Although it's quite a widely used term it's not a terribly useful one in all honesty(!) as it encompasses such a wide variety of styles, although the differences between them may not be observable to the casual observer. Social dance on the whole tends to be slightly less energetic than ceilidh dancing, and often contains more complex figures - if you think of the sort of dancing you see in the ballrooms in period dramas you won't be too far off!
There are a number of social dance clubs in Oxfordshire - mostly they meet on a weekly basis and charge a small subscription. The music varies from using recordings, through one or two musicians, to a whole band. Clubs are very welcoming to new members, including complete beginners - although one or two are specialist events and will expect a certain level of knowledge. If you've never done it before it's best to check the expectations beforehand. There will usually be a break for tea and coffee, and sometimes a bring and share supper.
The Oxfordshire Folk Association is an umbrella body co-ordinating social dance in Oxfordshire, and they often organise events in their own right. Their website also contains some useful information about the different styles of dance available.