Statuses are useful if simple checkbox is not enough for your needs.
Statuses available by default are: Open, In Progress, Done and Skipped. You can change that on Statuses page.
When statuses are enabled, the additional lozenge is displayed representing the status of the checklist item, as presented on the screenshot below:
A click on a lozenge opens a menu from which a new status can be easily selected:
Statuses dropdown can replace or accompany the checkbox, depending on the settings.