Quark is a fresh creamery cow's milk cheese, commonly used in Germany, Finland and other parts of Europe, somewhat similar to cream cheese. It is made by letting certain bacteria ferment milk, with the resulting curd. Some of the whey is removed to standardise the quark to the desired thickness. It is an acid-set cheese like "fresh" or "farmer's" cheeses, not a rennet-set cheese.
The word "Quark" is also used figuratively in German conversation as a word for "nonsense". Quark dazugeben means "to add your two cents worth" with a negative connotation. In this example, "Quark" is synonymous to the (more popular) "Senf" (mustard).
As for etymology, this word comes from mishearing and/or mispronouncing of Polish "twaróg" by German speakers (is pronounced almost like "quark" and means exactly the same thing).
For other meanings of the word see Quark (disambiguation)