While there wasn't 'a' currency in medieval times, there were many currencies. The right to mint coins was granted to various lords and cities or simply claimed by them. While the Holy Roman Empire had an official currency based on the the Reichsthaler (Thaler eventually becomes 'dollar'), many political entities inside the Empire coined their own money, including Hambur, Bremen, Lübeck, Bavaria, Vienna, Cologne, Schleswig-Holstein, and Strasbourg. (There were more.)
From the time of Charlemagne, French currency was based on the 'livre' or pound of silver. That was subdivided into 20 sous. The sou was divided into 12 denier. This did not stop various duchies, which were semi-autonomous for much of the Middle Ages, from minting their own coins. The 'livre tournois' was particularly stable and ultimately adopted by the French king as the basis of French currency.
The British pound sterling, like the French 'livre' and currencies in Italy, Spain, and Portugal, was equal to 240 pennies/Pfennige/denier — which just happened to weigh one pound. (Or were decreed to weigh one pound.) In the British system, 20 shillings equaled a pound. Each shilling was worth twelve pennies. A penny could be further divided into a half penny (ha'penny) and a quarter penny (farthing).
The modern decimal system is a rather late arrival.
Of course, barter and exchange were used as well, but currencies and coinage have been a part of European economics and finances since Roman times.
