How to make changes in HTML code and make them show up on site I am working on a Drupal 7 site that is being manged via Github. 

I am trying to change the HTML code on one page. The HTML that I am changing is in the [appname]/sites/all/themes/[app] folder. The HTML in this file is identical to what is on the page if I were to go to the [siteurl]/user/login then navigate to the page and press edit. However when I change the HTML on my local branch and push it up to github and then deploy it using heroku it doesn't actually change the page. 

My question is how can I change to way this page is displayed in code instead of changing the page on the drupal website itself.
Look into using the Features module. This way, you can convert any configurations that are stored in the database to code, push them up to the repository, and then pull and revert all the features on your test and production site. You can add template work as a custom feature as well. You should stray away from editing code in Drupal and lean toward creating custom themes, modules and features. I would be no where without this module.