It's basically Google drive or Dropbox but hosted yourself on your own server. It's an effort to set up and maintain but means it's entirely in your control.

It's a file sync platform. Say you have files you want to access from your desktop, you install next cloud and place the files there. They sync up with the next cloud server, presumably your NAS.

Now let's say you want to access those files from another machine. It could be a laptop, an Android phone, your friends, whatever. You just need to install the client and login, and there your files are, ready to sync to the new device.

Great use case would be syncing your computers user folders, such as my documents, desktop, etc. If you have to wipe your computer and start over, at least those items are preserved and easy to restore.

Otherwise sharing files with other machines in general is the main use.

I use it as a backup location for pictures and videos I make with my phone and for bookmark storage. But you can use it to fully replace cloud services like OneDrive, GCloud or iCloud.

Syncthing just... syncs things. Say you have a folder that you want to automatically get synced between devices, syncthing is exactly for this.

If you want something like Google Drive, you can run Nextcloud, which is like a self hosted Google Drive, but more powerful. You upload files, which get saved to the server, not just synced between devices. Then you can also sync them, sync calendars, news (RSS feeds), edit documents in it (assuming you install the correct extension), and a lot more things.