What is Double Entry?

Legal Definition
A term used among merchants to signify that books of account are kept in such a manner that they present the debit and credit of every thing. The term is used in contradistinction to single entry.

2. Keeping books by double entry is more exact, because, presenting all the active and all the passive property of the merchant, in their respective divisions, there cannot be placed an article to, an account, which does not pass to some correspondent account elsewhere. It presents a perfect, view of each operation, and, from the relation and comparison of the divers accounts, which always keep pace with each other, their correctness is proved; for every commercial operation is necessarily composed of two interests, which are connected together. The basis of this mode of keeping books, and the only condition required, is to write down every transaction and nothing else; and to make no entry without putting it down to the two agents of the operation. By this means a merchant whose transactions are extensive, comprising a great number of subjects, is able to known not only the general situation of his affairs, but also the situation of each particular operation. For example, when a merchant receives money, his cash account becomes debtor, and the person who has paid it, or the merchandise sold, is credited with it; when he pays money, the cash account, is credited, And the merchandise bought, or the obligation paid, is debited with it. See Single entry.
-- Bouviers Law Dictionary
Legal Definition
A system of mercantile book-keeping, in which the entries in the day-book, etc., are posted twice into the ledger. First, to a personal account, that is, to the account of the person with whom the dealing to which any given entry refers has taken place ; secondly, to an impersonal account, as "goods." Mozley & Whitley.
-- Black's Law Dictionary