You are not logged in as the database owner or as a user that is a member of the db_owner role. You will not be able to save changes to tables that you do not own. (Visual Database Tools)
Because you are not logged on as the system administrator, database owner, or a user that is a member of the db_owner role, you have limited privileges to the database. The privileges you have are determined by the permissions granted to your logon ID and the privileges granted to the roles that your logon ID is a member of.
Even though you are not the database owner, you will still be able to use any tables that you have permissions to see. For example, you can create diagrams using such tables. However you won't be able to perform all edits. Certain edits require SQL Server CREATE TABLE permission, which gives you permission to create new tables and modify tables that you own.
Even if you have CREATE TABLE permission, there are limitations to the modifications you can make. Remember, as you modify an existing table or design a new one, your work can induce attendant modifications in other tables. For example, if you change the data type of a foreign-key column, the corresponding column in the primary-key table will be automatically modified by the Visual Database Tools. If you do not own the primary-key table, and you are not logged in as the system administrator, database owner, or a user that is a member of the db_owner role, your modification will fail.
For more information, see Ownership Chains.