The guinea was originally an English gold coin, valued at 20 shillings (= one pound). It was made of gold from Guinea, and coined "in the name and for the use of the Company of Royal Adventurers of England trading with Africa" (cited in OED). Shortly after Scotland and England came together to form the United Kingdom (to be precise, in 1717), the value of the guinea was fixed at £1/1/0 - one pound and one shilling (£1.05 in modern terms).
There is no such coin these days. But the value still exists. "The guinea is the ordinary unit for a professional fee and for a subscription to a society or institution; the prices obtained for works of art, racehorses, and sometimes landed property, are also stated in guineas. Otherwise the word is now only occasionally used" (OED). To quote a price or fee in guineas thus represents a 5% premium over the same number of pounds. It is a way of marking professional status in Britain.