Have you had an account with Ancestry.com in the past? If so, you should know that generally such subscriptions automatically renew (which is in the terms and conditions). See this site for an explanation: http://www.familytreeshortcuts.com/avoiding-issues/subscriptions-automatically-renew/
In any case, they somehow got your credit card, and they definitely didn't go out looking for it (the BBB sure wouldn't give them an A+ if this were the case: http://www.bbb.org/utah/business-reviews/genealogists/ancestrycom-in-provo-ut-2003190).
Since it obviously wasn't your intent to subscribe, I'm glad that you caught it in time. It's never fun to find a random $155 charge on your card!