Before the public release of the internet, computer security was not much of a concern. For most businesses, they treated computers like other types of office equipment. Anyone could get onto a computer workstation or terminal, often without any type of user ID or password. However, things have changed, over time, and different types of security are needed to protect your data, including using digital certificates following the X509 [1] standards, for authentication.
Using X509 certificates for authentication processes will require you to use a certificate authority system. As the system creates a new certificate, it will create a new pair. Each pair is required, in order for authentication to work correctly. One certificate is retained by the organization and used on the system, which requires users to authenticate when connecting to it. The other certificate can often be shared with multiple users and is contained on their computer or other type of computing device.
Links:
[1] http://www.digi-sign.com/products#category_136