Bank Account 'Approved in principle' what does this mean exactly?

I've not the brightest of credit histories and have been banking with Halifax basic 'easycash' account for almost 2 years now. Me and my partner now live together and have done for 8 months so I decided to apply for a better account with a bank that has a branch near me as the local Halifax branch moved to another town! I applied at NatWest for their Current Plus account, and was surprised when it was 'Agreed in principle' what does this mean exactly? I find it hard to believe that I would get accepted. But I have been paying all my bills on time etc and have recently put myself on the electoral role at our first home together - would this of made a big difference to their decision? Can I still get rejected? Would be great to get back to a proper account with proper facilities.