Archived projects behave a little differently that other projects.
They won't show up in your searches by default and the project is essentially 'locked for monthly updates'. This means that you can't add monthly updates to it anymore.
However, you can still
Learnings from archived projects will still be visible in other projects that are tagged with the same tags. And as such, they will show up in topics.
The main purpose of archiving projects is to allow you to clean up those projects that are perhaps old and have been completed. While still retaining them somewhere should you need to refer to it in future.
You can restore the project by clicking on the link in the banner:
Or using the restore button in the right hand sidebar: