Typically speaking, the curd is the portion of milk proteins attracted to the coagulant rennin. Once separated the curd is put through a variety of aging and spicing techniques to arrive at different cheeses.
Curds however are not unique to cheeses. Sweet curds can be made by adding citrus juices to a mixture of butter and egg yolks cooked until the result is very creamy. These curds are then used as a topping for many dishes.
And lets not forget our friend Bean Curd, or as many of you know her, Tofu. Tofu is the iron rich curds extracted from soy milk in a process very similar to cheese.
As our young friend Webster so helpfully points out below, curds can be any coagulated portions of a liquid. If you think about, this includes things like scabs, Jello and lugies.