With "Blümchen" being the diminutive for "Blume" (flower) in German, "Blümchenkaffee" literally translates as "floret coffee", or "flower coffee". The word jokingly refers to very weak coffee. But why? There is a somewhat funny story attached to the origin of the German word.
So, there was a type of Meißen porcelain with a decor that was especially popular in the first half of the 19th century in Germany (an epoch often called Biedermeier). The porcelain had little flowers printed on the sides and at the bottom of the coffee cups. Now, apparently some of the bourgeois people who'd serve their guests with this type of porcelain would make coffee so thin that you could see the flower at the cup's bottom.
Resourceful as ever, the German Wikipedia page even provides a photo visualizing the phenomenon.
In its extended form, the concept of Blümchenkaffee stands for Scrooge McDuck-level avarice and unnecessary meanness, because the amount of money saved through serving your guests extremely thin coffee contrasts strongly with the expensiveness of the porcelain Blümchenkaffee is being served in.