A secondary SharePoint site collection administrator must be defined when creating a new site collection.
If a site reaches its maximum size, users will be denied access until an administrator fixes the problem. Having a secondary administrator reduces the risk of having a Denial-of-Service on a site. If the site reaches its maximum size, the secondary administrator can fix the problem if the primary administrator is not available. In some situations, having a secondary site administrator could be inappropriate for reasons of control or confidentiality.