Hi eDee,
I think by "app store", you are referring to both the Apple App Store (iOS) and Google Play (Android). I have no real world experience with development on iOS, but I can give you some pointers.
In broad terms, what happens after you have built an app in Love is:
(1) You convert the Love file into an Android and/or iOS compatible file;
(2) You go through the app submission process on Google Play and/or the App Store, and make any changes required as you go along to ensure the app meets the standards.
The process of submitting an app varies depending on the platform. Each platform has its own set of requirements and standards. Both Apple and Google have developed helpful, detailed checklists to help you understand the process and bring your app to store as efficiently as possible.
App Store (iOS)
The first thing you need to do is port your Love file to iOS. Basic instructions for iOS are available here:
https://love2d.org/wiki/Getting_Started#iOS. A second way is to "fuse" the Love file into an iOS app. Read about that here:
https://bitbucket.org/bartbes/love-expe ... ew-default.
For a guide on how to get published on the App store, read this blog post:
https://instabug.com/blog/how-to-submit ... app-store/
Google Play (Android)
The first thing you need to do is port your Love file to Android:
https://love2d.org/wiki/Game_Distribution#Android. There used to be another tool to convert Love files to apk, called "APKTool". If you come across it, it is important to know that
this tool is obsolete and shouldn't be used at the time of writing.
Once you have done that, read the Google Play "launch checklist" to get started:
https://developer.android.com/distribut ... -checklist. Work your way through the information carefully. It will take you through the entire process from start to launch.
Lastly...
To answer your question, apps are uploaded and hosted on Google/Apple servers. That is where it "lives". There are many reasons for that, but the primary reason is security. To a lesser extent, it is also because the stores would otherwise suffer from broken links and poor download speeds.
I am sure you already know this, but it is worth mentioning that Android users can download your app via your website directly if you want, as an apk file. It is therefore possible to circumvent the Play store completely, provided users enable installation of "unknown sources" on their Android device.
This isn't possible on iOS devices, unless they are jail broken, but only a tiny amount of devices are.