The loosely woven fabric that's useful for straining food is called cheesecloth. You can thicken yogurt by wrapping it in cheesecloth and setting it in a colander for a few hours.
Cheesecloth gets its name from its most common use, in cheesemaking. The gauze-like material is perfect for allowing moisture, or whey, to run out of cheese curds, leaving solid cheese behind. Cheesecloth is also useful in many other ways, both in the kitchen (covering food, straining soup) and out (wiping ink during the printmaking process, making lightweight clothing).