What is it?
Quark is a dairy product found in much of Europe: Germany, Denmark, the UK, the Netherlands, Belgium and France (perhaps elsewhere too, do tell me if you know more!). It is called fromage frais (fresh cheese) in French, platte kaas (flat cheese) in Flemish, and that is exactly what it is: a very fresh kind of cheese.
Quark is made by adding rennet or another souring agent (like buttermilk) to milk. The milk then separates into whey and curds. The whey is poured off or drained. The remaining curds are stirred until a smooth consistency is reached: this is quark.
What does it taste like?
Quark has a distinctive sour, slightly bitter taste that some people don't like. When sugar is added, this taste is somewhat hidden and the quark comes to taste more like yoghurt.
In the Netherlands quark is available in different flavours (plain or with fruit flavour) and with different fat contents, depending on the fat content of the milk it was made of. There is also 'cream quark', to which cream was added. Quark can be made of different sorts of milk, cow's, goat's or sheep's milk to name some, but most quark is made with cow's milk.
Quark can be used in many different recipes, sweet or savoury. In this it's very similar to yoghurt. You can eat it for breakfast or as dessert, with fruit and/or cereal, you can use it in quark pie, as a base for dips, you can add garlic and herbs and use it as a low-fat substitute for tzatziki or with a baked potato... it is even used in baking, the possibilities are almost endless.
But what if I don't live in the Netherlands?
This of course is a problem in itself...You could try making quark yourself if you need it for a certain dish and can't find it in a store. You need a recipe for making cheese (perhaps substitute the rennet in the recipe with buttermilk), and follow it up until the point where you have drained off the whey and should start pressing and salting and such. Just do the draining and then stir smooth the product you end up with, you'll have made quark. Unfortunately I've not managed to find any good recipes for this, so you'll have to experiment. Or you could make do with thick yoghurt.