Workspaces can be thought of as containers for boards. There are two ways to change the Workspace a board belongs to.
To move a board to a new Workspace you must be an admin of the board, and a member of the Workspace you are moving the board to.
Change the Workspace from the board menu
Open the Board menu and select Settings > Workspace name. Select the Workspace you would like your board to belong to from the drop-down menu. Members of a board will be added as Guests in the Workspace the board is moved to if they are not already members of the Workspace. In paid Workspaces, this would result in a charge if any of those members become Multi-board Guests.