A Surety is someone who agrees to be responsible for the debt or obligation of another. You'll see sureties in the old court records in the form of bail - a bond of money and sureties who would swear on that person's good behaviour until the next quarter sessions, and that they would reappear at court at that time. If they ran, the sureties were responsible and their money would be lost.
I've also seem them referenced in bastardy orders, where the sureties would be held responsible if the agreed upon child support was not coughed up.
In this case, I suspect it might have been a side-effect of one of his other crimes; either he had to find people who would swear to his good behaviour for the next six months, or they'd just toss him in the bridewell for that period. As it sounds like he wasn't the sort of gentleman usually found to be on his best behaviour, I guess he couldn't find anyone willing to bet on him keeping his word for that long.
Sounds like quite an ancestor you've got there! Have you looked at the Black Sheep Society?
