When you create a connection to use with a data source you are asked to set the owner of the connection. By default, if you are in organization then your organization is the owner of the connection. However, you can also set yourself as the owner making it a personal connection.
There are two compelling reasons for having most connections owned by an organization:
There is no loss of access to data when an employee leaves and their account is deactivated.
Federation across data sources is faster and more efficient if it uses the same connection.
Organizational-level connections are shared between admins of the organization and can be used by by all of them to create new live tables. Non-administrator users can only query and preview existing live tables.
Organization-owned connections can only be used to add data to datasets owned by that organization. If you are in organizations A and B, you cannot add data to a dataset owned by B using a connection owned by A.
With a personal connection, only the connection owner may create new live tables with the connection, and other members of the organization can query and preview live tables.