Well, okay, the word "hairy" itself doesn't need much explaining; but the more technical terms for calling a cap surface hairy do. The "hair"s on a mushroom are actually individual strands of hyphae protruding from a fruiting body, and yes, they're only a single cell thick. They have different names depending on their texture, numbers, and the visual effects they produce.
To describe the texture that results when these hyphae end up woven or matted together, several authors use analogies to fabrics, comparing the fungal texture to felt, flannel, or a woolen blanket. I have discarded these analogies, as it wasn't clear to me whether the authors were thinking of the texture of the hairs coming off of the fabric, or the main body of the fabric itself.
An ambiguous term. Snell & Dick(1957) seem to define this as a more general version of hirsute (i.e. any covering of stiff hairs), or perhaps like hirsute with but with shorter hairs. D. L. Largent(1986) defines it as hirsute with the hairs more flexible.
If the hairs are short (less than 1 mm) and soft, but not close enough to be velutinate, the surface is pubescent. The hairy covering itself is called pubescence.
I try to use this term as little as possible, so my site doesn't get blocked by those net censorship programs.