When you use the classic OneDrive web view in OneDrive for Business, you can drag files from the browser to your local computer, depending on your computer configuration. When you use the new OneDrive view in the OneDrive for Business web experience, you can't drag files from the browser to your local computer.
To work around this problem, do one of the following:
If drag-and-drop worked in the classic OneDrive for Business web view, switch back to that view. To do this, click Return to classic OneDrive in the left corner of the One Drive for Business webpage.
Use the One Drive for Business sync client to drag, drop, and synchronize files. To use the OneDrive for Business sync client, see Sync files with the OneDrive sync client in Windows.
Use the Open with Explorer command that's available in the classic OneDrive for Business web view. To use the Open with Explorer command, see How to use the "Open with Explorer" command to troubleshoot issues in SharePoint Online.
This is expected behavior in the new OneDrive for Business web view experience.
Still need help? Go to Microsoft Community.