How was marriage used as a political tool by the royal families of Europe?

Answer 1

A marriage in this sense basically meant an alliance (or atleast a softening of relations) between two factions.

Though i would like to mention that Henry VIII was not really concerned with such alliances. He was more concerned about having an heir. Henry's father had became King of England after a bloody civil war (The war of the roses) that started because there was no heir to the then king. Henry was determined to avoid this and became more and more desperate to get a male heir when his first wife only gave him a daughter, while he wanted a son.

Also note that in those times, royal families did not marry below their "class". A royal marriage to someone below high noble status was considered scandalous. This created a situation were royals and nobles would always look for the most advantagious marriage possible. Love was not an issue

Answer 2

Marriage was usually used to either ally two families against a common foe: France and England vs. Spain in Henry VIII's time.

Or a marriage between two royal children was part of a treaty: Henry V and Catherine of Valois.