The RSGB stands for Radio Society of Great Britain. It is the official UK society for amateur radio users, or if your American ham radio.
It is a non-profit organisation that issue the licences to amateurs in the UK to allow them to broadcast. They also organise clubs around the country.
More importantly they offer loads of services to its members. Including a monthly magazine, book discounts, advice, insurance, contests, awards and a bulk QSL card exchange service.
Membership to RSGB is open to all that are interested, but you do need to pass a theory test before they allow you on the air.