Bechamel sauce is one of the 5 basic sauces described by August Escoffier in his epochal standard work Guide Culinaire at the beginning of the 20th century.
The sauce is certainly best known as the main ingredient in lasagne. It also seems that béchamel sauce was originally invented in Italy and then made its way to France with the marriage of Catherine de Medici and her court chefs.
Basically, 2 factors are decisive for a perfect béchamel:
Firstly, the milk has to be cold so that a perfect connection with the Roux occurs. And secondly, you have to stir long enough for the sauce to become creamy and lose the floury taste.