These are Tasks assigned to you.
In case the task is late already or is going to be late based on current estimations, it will be marked red.
The order of tasks that defines their relative priority is your personal preference. It doesn’t affect project planning. To learn more about what affects project plan, read about Automated Priority Based Planning.
Fill in time spent on tasks to get prepared for Timesheets submission or update Project Manager on task progress. Logging time spent reduces “remaining work” and Project Manager can see that.
All the people following the task will be notified on any changes to make. If you want somebody get notified, just add him to followers.