Upgrading to a new version of WordPress only changes the core files and does not touch any other files such as themes and plug-ins. You might want to check whether your plug-ins are compatible with 3.6. Base themes (such as the newly introduced 2013) will only install fresh together with a major update but will not automatically update with a WordPress update. Theme updates are seperate.
Normally, your theme should work fine in WP 3.6. If you are really worried, make sure to have a back-up of all your content.