When a checklist is started you can assign or unassign people from the checklist.
To assign people to a checklist open the checklist page and click on the icon with a user and a plus sign on the right side of the assigned people in the header.
This will open a flyout with a list of people in the team that is not currently assigned to the checklist.
Assign people by clicking on the people in the list.
When persons is assigned to a checklist they will be notified by email that they been assigned to the checklist.