When you user Project Server, if you want to save any change, the project plan needs to be checked out.

Once you end your work, It's recommended to check in the plan before/while you close the plan.

In Microsoft Project App.

How to check is the plan is well checked in and make sure no one checked out in the meantime?

In Project Web App, you can go to this page :

If the project is not on the list, then, it's checked in.