I think most people have already covered what the basic idea about "points" means, but I'd just like to add that they don't really matter to you as a student, as they are just used for the school's league tables, so that they can essentially use statistics to "sell" their school to prospective students thinking about starting in Year 7 etc. on open days.
While the "equivalent marks" are just the UMS conversions (not the raw marks). I've found that for whatever reason, Edexcel Maths have chosen to not display our UMS marks on the results sheet, and I've heard of how some English Language exam boards have also done the same. It's a little strange. :s