A ticket’s owner is simply the agent that is currently responsible for it.

Whose job is it to assign tickets?

It depends on your organization’s workflow, but in most cases, you will assign tickets to yourself when you choose an issue to work on from the pool of new tickets.

In principle, any agent may assign a ticket to any other, as long as both have the required privileges for the ticket’s group.

Why would I want to re-assign a ticket to someone else?

Sometimes, complicated issues will require a ticket to be passed back and forth between multiple agents before it can be closed. In such cases, a colleague may assign a ticket to you (or vice versa) after it has been partially resolved.