Site owners may download the contents of a SharePoint Online document library. If you want to migrate lots of SharePoint Online files, Microsoft recommends syncing the libraries or folders. Then you can use File Explorer on your computer (or Finder on a Mac) to move the files to the new location. For more information about syncing SharePoint files, see SharePoint Online: Sync SharePoint files with your computer.

If you want to download only a few files or folders, you can from your browser:

1. Click on the file or folder in a SharePoint library you wish to download.
2. Once selected navigate to the command bar, and select  
3. Depending on your browser you may be prompted to specify a location of the Download.