The oldest that archaeologists have found that looks like draughts - a loam plate which is divided into squares - is 5000 years old. The game was played with cone-shaped stones. There is no consensus on whether this game should be called the first draughts.
The queen of the French medieval chess gave its name to the game, "fierges". Later the queen was called "dame" (lady) and the game was named "jeu de dames". In Dutch it became "Dammen" and in German ''Damenspiel''.
The English draughts originated in the 12th century. They used the stones of Backgammon a board with 64 fields and the moving of the pieces from the game Alquerque, an Egyptian game. The original checkerboard has 64 squares (now known as the little board), but in 1723 there was a Pole in Paris who created draughts on a board of 100 fields. It is called Polish draughts and this is what we play nowadays, usually called International Draughts.
The story goes that Napoleon and his soldiers found it a great game and took it on their campaigns. This way Polish draughts became internationally known.
In the Netherlands they played English draughts since the 16th century, later also Polish draughts.
More information: http://www.draughtshistory.nl/