lafetech
You only need to check the page when you want that template style is applied to that page.
For example, at this moment, you have JA Decor - Default is default template style which means that all pages will inherit this style, even you check or not.
But if you want to assign JA Decor - Yellow template style to a specific page, i.e 'Accueli', then this page will have style of this Yellow style.
The same with other template styles, you can assign to the page you wish. All other pages which are not checked will inherit default template style.
I hope this makes senses.