What “fine as frog hair” means
The phrase has two meanings, and both rely on a pun on the word "fine". Wiktionary lists it as a colloquial simile meaning extremely fine, in the sense of slender or delicate. The Phrase Finder records the other, more common use: "fine" meaning excellent, as in "How are you?" "Fine as frog hair."
Either way, the humour is the same. Most frogs have no hair at all, so anything as fine as frog hair is too fine to see.
Where the saying comes from
The Phrase Finder describes it as an American simile from the mid-19th century, and its earliest example is an 1865 diary in which the writer says they are in high spirits, "as fine as frog's hair". It survives mostly as a folksy, rural expression, and folklore collections link it with the South and Texas.
There are playful extensions, such as "finer than frog hair split four ways", which splits a hair that does not exist. A related Southern saying, "slippery as frog hair", is used for something hard to pin down.
Do any frogs have hair?
Almost none. The Phrase Finder notes one exception: the so-called hairy frog of Central Africa. Its males grow hair-like strands of skin in the breeding season. They are not true hair, which keeps the joke intact.
What truly fine hair is
In hair care, "fine" describes the width of each strand, not how much hair you have. One dermatology study classes hair under 60 micrometres across as fine; in a study of women's scalp hair, strands ranged from about 37 to 111 micrometres. So the finest human hair is roughly a third the width of the coarsest.
Fine is not the same as thin. Thin, in most people's use, means low density: fewer hairs. You can have fine hair and plenty of it. Fine vs thin hair explains the difference in detail.
How to tell if your hair is fine
Take a single shed strand and roll it between your thumb and finger. If you can barely feel it, or cannot feel it at all, your hair is fine. Compared with a piece of sewing thread, fine hair is noticeably narrower.
Other signs: hair that goes flat a few hours after washing, gets oily quickly, slips out of clips, and will not hold a curl for long. None of these is a problem in itself; they are just how fine hair behaves.