Without media-discontinuity or any delays an operator of a web-shop is able to verify your identity or your age.
Because of that you will receive ordered goods earlier or make use of ordered services immediately. Since e-id is based on the infrastructure of the online-banking of your bank you use a well known and trusted environment.
Furthermore it uses highest security-measures to protect your personal data from access by third parties. And last but not least the service is free of charge.