What benefits does automation bring to system administration?

Fewer errors from manual work, fast and correct provisioning, repetitive tasks done automatically, more time for important work, and faster rollout of new applications and updates.

• Avoids errors caused by manual administration.
• Fast, correct provisioning and configuration of systems: a new server is configured in minutes and the same way every time.
• Repetitive tasks are automated, such as user accounts, patches and log rotation.
• More time for important work, because the admin is no longer the one typing the routine steps.
• Faster delivery for the business: the next version of an application or an update to a service can go out sooner.

The last point is why management cares. Automation is not only about convenience for admins, it shortens the time between "the change is ready" and "the change is live".

Go deeper:

• What is IT automation? (Red Hat) — lists the benefits: fewer errors, scaling, faster delivery, consistent governance.
• you need to learn Ansible RIGHT NOW!! (NetworkChuck) — energetic hands-on demo of how much time automating routine admin work saves.