Re-posted from the Veronica Foods blog.

Mother of vinegar – also called Mycoderma aceti (a New Latin expression, from the Greek μὑκης (fungus) plus δἐρμα (skin), and the Latin aceti (of the acid) – is a substance composed of a form of cellulose and acetic acid bacteria that develops on fermenting alcoholic liquids, which turns alcohol into acetic acid with the help of oxygen from the air. It is added to wine, cider, or other alcoholic liquids to produce vinegar.
Mother of vinegar can also form in store-bought vinegar if there is some non-fermented sugar and/or alcohol contained in the vinegar. While not appetizing in appearance, mother of vinegar is completely harmless and the surrounding vinegar does not have to be discarded because of it. It can be filtered out using a coffee filter, used to start a bottle of vinegar, or simply left in and ignored.