Tobias Snape is Severus Snape's father. He married Eileen Prince. Little is known about him, but it is possible that he appears in a scene which Harry sees in Snape's memory during Occlumency lessons. Harry sees a hook-nosed man towering over a cowering woman. This is an unexplained scene from Severus's past, but one which may be presumed from the circumstances under which Harry sees it to have some significance for Severus. The limited description fits what other facts are known about Severus, that he seems to have grown up in a muggle area with a muggle father. Eileen is known to have attended Hogwarts and to have been a witch.
In Harry Potter and the Deathly Hallows we learn that Severus's family often had arguments, and that it was an uncomfortable place to live. Severus remarks to his friend Lily Evans that his father "doesn't like anything", least of all magic. The thought of leaving his father to attend Hogwarts seemed to enthrall Severus.