Religion played a really key role in everyday society and the parish Church (the local church) was the focal point of societal life, highlighting the importance of religion.
The Church was led by the Pope, but he had such a vast number of countries under his control, that his actual influence in England was very little. This meant that Henry, as king, had some power of the Church.
Henry VII's influence over the English Church:
the right to appoint Bishops and other Clergy.
had the right to use the Church's wealth to reward political allies (like Thomas Morton). This was really important at the start of his reign (1485 - 1490) when he was unstable.