Before you could update the theme, you must enter purchase number you got from ThemeForest. Navigate to Appearance > Theme Options > Theme Information & Update then enter purchase number and save the changes. To check if there are any updates of Billio Theme, navigate to Appearance > Themes There will be Update Available link on Billio thumbnail if there is an update version.
IMPORTANT : Please make a backup to the Theme Options’ settings before you update the theme. you can follow this guide to create a backup to the Theme Options’ settings : http://kb.detheme.com/knowledge-base/create-theme-options-settings-backup/
Click Update Available link then click update now link on popup window to start updating the theme.