What does 渋い Shibui mean?

Shibui (渋い) began as the taste of an unripe persimmon and became an aesthetic term for beauty that is understated and precisely sufficient.

Written
渋い (shibui)
Literally
Astringent or sour, as an unripe persimmon is. From roughly the Edo period it also names beauty that is restrained and exactly sufficient.
As slang
Both senses are live. The same word describes a bitter taste, a sour expression, and a piece of craft admired for refusing decoration.
In anime
The older character with an understated coat, the plain object that turns out to be the expensive one, the design that declines to be striking.

Shibui describes a taste and an aesthetic. The taste is astringency, the pucker of an unripe persimmon. The aesthetic is beauty that is restrained, unshowy, and exactly as much as it needs to be.

From the mouth to the eye

The word appears in its earlier form during the Muromachi period, meaning sour or astringent. By the early Edo period it had begun doing aesthetic work, and the townspeople of Edo used it for song, dress and craft that pleased by understatement rather than by display.

The bridge between the two senses is legible. An astringent flavour is not sweet, does not ingratiate, and rewards a palate willing to meet it. An object described this way behaves the same: it does not flatter, and it becomes impressive on inspection rather than on sight.

The precise claim

Not merely plain. The standard is that a thing is exactly what it was meant to be and has not been elaborated beyond that, which is a harder target than simplicity: an object can be simple by being unambitious, and this requires that nothing necessary is missing either.

The noun form carries a further sense of depth, which is why the word attaches to things that improve with acquaintance rather than things that impress immediately.

Where it sits beside wabi and sabi

They are neighbours and not synonyms. Wabi-sabi concerns austerity and the beauty of age. This concerns restraint and sufficiency, and does not require anything to be old or worn: a new object, perfectly made and refusing ornament, qualifies.

The three together form a vocabulary for admiring what has been left out, which English possesses only in fragments.

The modern everyday use

It is also a compliment about people, and it skews to older men: a person described this way has an understated quality that does not seek attention. It can also mean a sour face, and the two uses live comfortably side by side.

English understated is close and colourless. Classy is wrong, since it implies expense. What English lacks is a word carrying the flavour of astringency inside the compliment, so that the praise itself refuses to be sweet.

Quick answers

What does shibui mean?

Astringent or sour, as an unripe persimmon is. From roughly the Edo period it also names beauty that is restrained and exactly sufficient.

Is shibui an insult?

Both senses are live. The same word describes a bitter taste, a sour expression, and a piece of craft admired for refusing decoration.

What does shibui mean in anime?

The older character with an understated coat, the plain object that turns out to be the expensive one, the design that declines to be striking.