Brian Williams, also known as Brian Pond, is Rory's dad and Amy Pond's father-in-law. And although we haven't seen him meet her, he is also River Song's grandfather. A down-to-earth guy who according to Rory hated travel, he was whisked away on a trip with the Doctor and grew to appreciate the wonder and potential in new places. Brian quickly adapted to the type of mad adventure his son Rory was already familiar with...so much so that he eventually went on to journey the world and beyond.
Clearly very fond of Amy, he did have the tendency to be picky and less than confident in his Rory's abilities. Yet, during his time on the Silurian ark, he bonded more closely with Rory and saw his son's medical skills and coolness in the face of adversity in action when Rory was able to patch him up after a blast from one of Solomon's robots.