Where credit cards or loans use a representative APR, this means that 51% of successful applicants will be given the stated interest rate.
With credit cards, the rate for purchases (as opposed to balance transfers or cash withdrawals) is used as the main rate to advertise the card.
So if that is described as 19.9% representative APR, then 51% of people accepted will get 19.9% APR, but 49% will get a different rate (likely to be higher).
Loans are slightly simpler as they only have one rate. So if a loan is advertised as being 7.5% representative APR, this means 51% of accepted applicants will get 7.5%, and 49% will get a different rate (likely to be higher).
Of course, some people will be rejected outright for the card or loan too.