Sort contents in content list
To add Sort functionality using Drag and Drop into admin/content section, you need to play with administration views using Admin Views module. Note that Weight module is also necessary for this. After installing and enabling these module you can edit administrative views under admin/views section.

But if you simply want to add your new views of specific contents then there is already Weight view available under admin/views section. You can check this view to see the working and functionality using Drag and Drop. 

Note: Weight module must be enabled for contents to be sorted.