King Henry VII was first English King from House Tudor, and the father of the series' main character King Henry VIII. He never appears (having been dead years prior to the show's timeline), but he is mentioned several times. As the last champion of the House of Lancaster, Henry VII (then known as Henry Tudor) gained his throne by narrowly winning the Battle of Bosworth Field, the last battle of the War of the Roses; he then cemented his control over England by marrying Princess Elizabeth of House York. He kept peace with nearly all his neighbors throughout his reign and was a careful and frugal administrator, allowing England to recover after decades of civil war.
In series one, King Henry VII is briefly mentioned by his son, the present King Henry. He is evaluating his marriage with Catherine of Aragon. He says that once Catherine's first husband (Henry VII's son and Henry VIII's brother) Prince Arthur died, Henry VII arranged for the then Prince Henry to marry Catherine so he would not lose her dowry.
When the North rises in rebellion in 3x01, King Henry VIII reminisces about the Cornish rebellion against his father in 1497.