iCloud & iCloud Photos · Desktop & Documents in iCloud
Why do files on my Desktop have cloud icons?
Short answer: Your Desktop is syncing to iCloud (Desktop & Documents Folders) and those files are online-only. They download when opened; use Download Now or Keep Downloaded to keep them local.
Because your Desktop is syncing to iCloud and those files are online-only. With Desktop & Documents Folders on in iCloud Drive's settings, Desktop files are iCloud files, and with Optimize Mac Storage on, macOS can free older ones. A cloud icon means the file is in iCloud and downloads when you open it.
If you'd rather keep everything on the Desktop local, right-click the files and choose Download Now, or use Keep Downloaded on recent macOS. To stop syncing the Desktop entirely, see turning off Desktop & Documents — read what happens to your files first.