If you are trying to open project plan and it appears as checked out in the File-> Open dialog box, it means your previous connection to project server was interrupted or if Project Professional is closed abruptly before you can check in a project.
You can force a check-in of your own project by using the "Check in my project" link in the Project Center.
- On PWA home page, click on Projects link from top menu
- On left side pane, under Actions -> click on Check in my projects
- Select your project name from list and click "Check in"
Please note, this feature only to check in projects that you checked out by you; you can not check in project that was checked out by another user. Only a Project Server administrator can check in a project that is checked out to any user.