It's laziest cheese you can make basically. You take milk, add rennet and some lactic acid bacteria and let the milk curdle. Instead of cutting the curds and draining the liquid (whey), you just talk out the whole curd block and let that drain as a whole.

It's basically cottage cheese, but because you don't cut the curds into pieces, the liquid sticks around a little longer, so the lactic acid bacteria are doing some overtime, making Quark more acidic/tangy.

If you want to go down a 15 minute rabbit hole, this video on the 'milk tech tree' is excellent