This is a stinkhorn mushroom, or a phallus impudicus. An amazing fungus which will actually grow rapidly before your eyes if you happen upon it as it emerges from the ground. The spores are dispersed from the veiled structure called a gleba.
The name, stinkhorn, is very apparent when you physically encounter it. You will never forget the smell and that is part of the survival strategy of the plant. They attract flies, which disperse the spores.
The immature fruiting body is actually quite edible and tasty, with a radish like tang. They are like white eggs and can be eaten raw or pickled as they are here in France and Eastern Europe. In fact, the "eggs" are used as a flavoring in regional seasonal sausage recipes!