Fealty is a promise between two people to be friends and protect each other.
Homage is a promise by one person to let another be in charge.
So two friends might swear fealty so that everybody knows that if you mess with one, you're messing with both. A King would have his officers swear homage so that everyone knows that they work for him. When an homage is made, it is made with a fealty, so that the person who gives the orders is bound to treat the person who takes the orders as a friend. A person who has sworn fealty and homage is known as a vassal. As a lord or vassal you make sure that the vassal stays out of trouble and has a good time.