A Microsoft file hosting and synchronization service.
OneDrive is cloud storage: a place on the internet where you can store files. OneDrive is simply Microsoft's branded cloud storage, just like Google Drive is Google's branded cloud storage and iCloud is Apples' ... you get the idea. They're all the same thing: a place on the internet to store files. Think of it as your personal hard drive on the internet.
The OneDrive app is different. That's an app that helps you work with your cloud storage. For example, the OneDrive app lets you sync your files with your OneDrive or backup your files to your OneDrive, if you want to. Nobody has to sync their files with their OneDrive, or backup to their OneDrive. You can if you want to. Google has its own Google Drive app which works the same way.
The truth is, nobody needs an app to access their cloud storage. You can upload files to your cloud storage or download files from your cloud storage completely on your own. No app needed.
To use cloud storage effectively, you have to decide which of your files you want to keep in the cloud, which you want to keep on your computer, and which you want to sync between your cloud storage and your computer. Nobody has to sync anything at all, but it comes in handy from time to time.
The problem with the OneDrive app - not everyone thinks it's a problem, and they're entitled to think like that - is that Microsoft sets up the app to automatically sync all your files. Whether you want that or not. Whether you understand file syncing or not.
File syncing means that everything you do with a file in one place, whether in the cloud or on your computer, is automatically replicated in the other place. Created a file on your computer? It's also created in your OneDrive. Deleted a file in your OneDrive? It's also deleted on your computer. This is what messes people up. Things happen to their files that they weren't anticipating and never wanted to happen.
By explaining all this I hope I have helped you understand what's going on with your files when you move them or change them. And how to use the OneDrive app to your advantage, if you want to use it at all. No one has to sync their files, and no one has to backup all their files to cloud storage. You can if you want to, but my suggestion is not to do that until you have a good understanding of how file syncing works.