Loyalists wanted to remain being a colony of England and british citizens. Many of them had british relatives or ancestors and didn't want to fight against England army. Others had business deals which would have been affected by the war and the independence.
On the other side, Patriots wanted to put an end to British domain on the thirteen colonies and fight to be a free country called United States. They didn't like not having any saying on how to rule their land and the taxes they were forced to pay to England. British delegates mistreated them and so Patriots united to face the colonists to fight for freedom.