Issue Checklist offers its own Checklist History tab with the pretty formatted list of all checklist changes.
If you still want to see the checklist changes in the standard Issue History tab, please read below.
In order to see the list of checklist changes in the issue history, please open the History panel on the issue page:
Tracking all changes in issue history is disabled by default. It can be enabled by switching off the "Save checklist data to Jira custom fields" toggle in Global Settings page.
Changes are tracked as the Issue Checklist user. If you would like to see a real user data, please visit Checklist history tab.