When you change the owner of a task, you in a way re-assign the task to someone else.
To change the owner of a task:
Note: Task owners can be changed only by, well, the task owners themselves or by users with Administrator roles.
Open a task.
Click on the Owner icon and select a new owner.
Note: When you change a task owner, the new owner will receive a notification.
Next: How to re-assign a task?