First, keep in mind that you aren’t meant to edit a theme directly. WordPress’s Appearance > Editor presents security risks, and can allow you to modify things in a way that breaks your site, so it is best to disable it entirely. Any time you modify a theme, and then update that theme, all of your changes will be lost.
Instead, create a child theme, where the only real required files are style.css with comments that let WP know it is a child theme, and then whatever files you want to override. This will allow you to continue using and updating your theme, but apply a few changes here or there as needed.
Different themes use different files to control the homepage, especially depending on whether you are using a Page as your front page or a traditional list of Posts. Some themes may use front-page.php or home.php if you are using a traditional list; if you are using a Page, there are a variety of Page templates such as plain old page.php, or more specific ones like page-slug.php, page-id.php, or even a template such as tpl-custom-page.php. The WP template hierarchy explains all the possible theme files and what order they are used in – the Visual Overview is especially helpful in cases like this where you’re trying to track down which specific file is being used. It is also possible to use various plugins which can show you what template is being used for a particular URL’s display.