A surety is 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.  As an example, if John Jones signs a bond to act as administrator of an estate, but does not, it becomes the responsibility of his surety. Being a surety was not to be taken lightly.
 Henry Campbell Black, Black's Law Dictionary, Fourth Edition (St. Paul:1951), West Publishing Co. http://www.eogen.com/SuretyIndex, accessed 14 Jan 2017.
Published 2 March 2017, Western Kentucky Genealogy Blog, http://wkygenealogy.blogspot.com/