Houses, or families, are very important factors in the Game of Thrones. A House sticks together as they are truly the only ones that can be trusted. Houses will form allegiances in times of war and need to protect the interests of the Houses or the Kingdom. The leader of the House is either the oldest member of the house or the most respectable. In most cases it is a man, but in rare cases the head of a House is a woman.
Each House is represented by something. Most commonly is an animal, but it can be something else.
In VERY rare circumstances someone can denounce their House and change their name making their own House, but it will require to almost completely start over politically as turning on your family is one of the biggest crimes you can commit.
Not everyone has to start their own family, in fact we encourage you to join Houses that are already formed as a family member. Sometimes relatives are distant.