To apply template to the storefront click the button
To edit template logo, favicon, thumbnails sizes click the edit button
Third party templates you can find more settings and dependencies in the template's extension page
In the store's Admin area go to the Extensions > Templates section and check whether the your new theme extension is installed and enabled at your store. If not you can not manage this template in Design > Templates section.
Changing template Layout
In the Admin area go to Design > Layouts
If you are looking how to disable, edit or move some blocks (side boxes) in the Admin area go to Design > Layouts section. Then select your store default template.