The universal veil is a layer of tissue that completely surrounds the baby mushroom (in some species), making it look like an egg at first (or, more dangerously for the edible-mushroom hunter, a puffball).
When the mushroom grows, it breaks out of the universal veil, leaving bits of it attached to various parts of the mushroom.
A universal veil that hangs together like a skin is said to be membranous. The bottom half of a membranous universal veil is often left behind at the base of the mushroom's stalk, forming a sort of a cup that the mushroom seems to be growing out of. This remaining universal veil tissue at the base of the stalk is called a volva, and the projecting part of the volva is called the limb. A volva possessing a limb is called limbate, and the edge of the limb is called the rim of the volva (it is sometimes called the margin, like the edge of the pileus, but I am only using the words in this mutually exclusive senses in this website). A deep volva that is shaped like a cup or sack is called a saccate volva.
A non-limbate volva is clamped tightly to the stalk, and its rim merely separates a small distance or rolls down a bit at the top, like a sock. Such a volva is called peronate, or ocreate.
As used here, this term is completely distinct from caligate, which is a similar clamped-to-the-stalk characteristic of the partial veil.
Part of the universal veil can also be left plastered to the cap surface, either as a large central patch or as bits of material that get more and more separated from one another as the cap expands. You will sometimes see these little flakes or bits referred to as "warts" on websites or the more popular literature.
The universal veil can also be powdery. Here, yellow universal veil material (the stuff on the cap is white because it has bleached in the sun) has formed a powdery coating on the base of this mushroom's stalk.
See the entry on powdery for more precise terms (I pretty much just use powdery in this website).
A universal veil may also consist of a layer of slime. In this case, the slime usually coats the stalk and the cap after the mushroom has opened. I don't know of any special term for this and just call it a slimy universal veil in this database.