Theme options is a custom admin page which comes with some WordPress themes. It allows users to change theme settings without modifying theme files or touching any code. These theme option pages can be very simple with a handful options or it can have tons of customization options split into either tabs or multiple pages.
Twenty Eleven, one of the WordPress default theme, has a Theme Options page that is extremely simple.
It is important to understand that WordPress themes are NOT required to have an options page. For example, Twenty Twelve, one of the default WordPress themes does not have a Theme Options page. Instead it uses the WordPress theme customizer feature which allows users to customize their themes with a live preview.
There are themes like Headway Theme that adds their own live drag and drop editor which a lot of WordPress beginners find to be helpful and attractive. Other theme companies come with their own branded options panel that allows for a lot more customization, but they are not drag drop. Some people prefer it this way. Example of theme companies that have very elaborate theme options panel are Elegant Themes or Themify.
Theme options are good for most users, but they do tend to complicate things on the development side of things. This is why many developers prefer to work with theme frameworks that have simple theme options panel like the Genesis Framework.
