From your question it seems like you are missing/not fully understanding the concept of templates. A template contains the include of the header.html and footer.html. The page only contains a reference to the template. This is the way Jekyll prevents the repetitive work of adding the include to every page.
Ideally the page is a (index).md file with frontmatter like this:
---
title: Title of the page
layout: template
---
Lorem ipsum
The template file is called template.html and resides in the folder _layouts. It looks like this:
{% include header.html %}
{{ content }}
{% include footer.html %}
Hope that helps!