In general, a person who assumes the responsibility (is "bonded") by the court to pay money or do other ordered acts on behalf of his "principal" who was charged with that expense, or the performance of that act, if that principal should fail to do so. Typically in genealogy research, we find a surety named wherever the losing party in a court decision appeals (the Appellant). The surety guarantees that if the appeal fails, the appellent will pay the original fine plus court costs.
Source: Black's Law Dictionary, 4th Edition.
A term often used to indicate the researcher's assessment of the quality of the evidence.