The partial veil, which becomes the annulus or ring on the stalk in the mature mushroom, is a swath of tissue (in yellow in the picture) that covers and protects the gills of the fruiting body while it is developing. As the spores mature, the cap expands, tearing away from the partial veil, which is left hanging on the stalk.
A flaring annulus is one where just a few points on the edge of the annulus remain attached to the rim of the cap after the rest of it have pulled away; this gives the annulus a very uneven appearance. The mature annulus in the picture is flaring (attached to the cap only at the very right). Many of the other pictures for this topic also show a flaring annulus.
This picture illustrates something else: sometimes the partial veil's point of attachment to the stalk is at its very base, instead of high up. In this case, the entire stalk (below the point of the ring) ends up covered with pieces of partial veil, and the ring ends up pointing up from the stalk (like a loose sock), rather than hanging down from it. The stalk in this case is said to be caligate, or booted, and the ring used to be called an armilla, rather than an annulus, and I am reviving the term since it comes in handy sometimes: for instance, many mushrooms now in the genusTricholoma used to be in a genus typified by this character and named after it: Armillaria. Why they're not there any more is another story, but in any case the armilla rather than an annulus is a useful way to help distinguish them from other white-spored genera with a partial veil, like the Lepiotaceae.
A partial veil that really holds together can be described as membranous, just like a universal veil. One that is clearly composed of separate fibers that can be easily pulled apart from one another (like a cotton ball) is called cottony. And a fragile veil composed of strands so separate that referring to them as one collective object is an act of will is called fibrillose.
The picture is kind of nice, because it lets me say that the veil is cottony near the stalk, becoming fibrillose near the capmargin.
Another term for this sort of cottonyveil is submembranous, meaning almost or not quite membranous. I use cottony instead of submembranous in this website.
An extremely fine, fragile veil with a cobwebby texture is called a cortina. In the specimen at the center of this picture, a few strands of it can be seen extending from the stalk to the left of the cap, and broken strands are visible as a fluffy brown mass on the stem. A cortina is one of the major features of the genusCortinarius, and the threads of the cortina often catch its brown spores as they drop, making them visible as fine brown streaks along the stem.
A partial veil may also consist of a layer of slime. In this case, the slime usually coats the stalk after the mushroom has opened. I don't know of any special term for this and just call it a slimy partial veil in this database.
