"Notify when a Task is toggled" controls whether JIRA notifications are triggered when a task changes
state (checked or unchecked). If this option is enabled (yes by default), and your instance has
a Notification scheme setup, then user are notified when tasks are toggled based on the notification
rules you've setup.
"Fire Issue Events" is disabled by default, and controls whether an issue update event is fired
when a task is toggled.
This typically only matters when you have other add-ons that you want to notify when tasks are changing.
We have only encountered a few scenarios where this mattered, and it usualyl involved custom add-ons that
clients have written to integrate with Simple Tasklists.
Most other users / JIRA admins most likely don't care about this setting.
This setting does not impact the use of Workflow functions, but it does impact the use of
the JIRA Automation plugin, and can have interesting side effects if you have automation rules that
are tied to issue_update events.
"History entry for Task changes" controls whether a history entry is generated whenever
a task is added, edited, or removed. History entries are kept separate from the standard issue history,
and do not show up in the JIRA Activity Stream, or the regular issue history. Instead, Simple Tasklists
exposes it's own history tab within each issue.
"History entry when a Task is toggled" controls whether a history entry is generated when
a task is toggled to checked or unchecked. Each history entry identifies which task was toggled,
who did it, when, and the new state of the task.