Born and raised in Inuvik, Northwest Territories, Floyd has served his community in a number of roles beginning in 1991 as a board member of the Inuvik Hunters and Trappers Committee and the following year being elected to Town Council as councillor before being appointed as Deputy Mayor.
Floyd was first elected to the NWT Legislative Assembly in 1995 as MLA representing the riding of Inuvik Boot Lake. Floyd served four terms as a Member of the NWT Legislative Assembly serving in a number of capacities including Committee Chair of Governance Economic Development. He also held a number of portfolios as Minister including Health and Social Services, NWT Housing Corporation, Public Works and Services, Public Utilities Board, Northwest Territories Power Corporation, Finance, Financial Management Board, Aboriginal Affairs and Intergovernmental Affairs. He retired from Territorial politics as Premier of the NWT in 2011.
After returning to his hometown of Inuvik, Floyd was elected as Mayor in October 2012. As Mayor, he continues to work to create a sustainable economy for Inuvik and surrounding northern communities.