An affirmation ; a positive assertion; a solemn declaration. This word is seldom, if ever, used for a declaration made under oath, but denotes a declaration accompanied with solemnity or an appeal to conscience.
Law Dictionary – Alternative Legal Definition
The proof which a man gives of the truth of what be says, by appealing to his conscience as a witness. It differs from an oath in this, that by the latter he appeals to God as a witness of the truth of what he says, and invokes him as the avenger of falsehood and perfidy, to punish him if he speak not the truth.