Club 10 is an effort by Slimming World to mark and recognise the importance of loosing 10 per cent of your body weight. It's seen as a milestone and, for those with quite a bit to loose (more than, say, a stone or two): it is the first target you work towards at SW.
The reason for this that SW recognise, as a result of a number of studies over a number of years, that there are significant health benefits to loosing 10 per cent of your body weight. It means that the instance of diabetes, heart disease, asthma and so on are reduced quite dramatically.
In practice, it doesn't actually mean that much in my experience. It's your first target (once you've achieved Club 10, you choose your own target with information from your Consultant and the SW literature etc... you can set an 'interim' target if you want) and when you've got it you get a sticker and a certificate and a bit of fuss made of you at group.
Once you've gone to group you'll see there's a couple of references to it in the booklets you get and on the website where you can read more.
Basically, it's a good thing to achieve, the more people that achieve it the better as far as SW are concerned (it helps them argue to the NHS to get more SW prescriptions etc) and you get a sticker.