How exactly web apps (HTML5) apps run on smartphones as a native app?

If you use Bootstrap/JQuery you it can automatically adjust a website to any phone, tablet, and/or device(s). Also personally as a Web-Developer I test across different platforms, browsers, and resolutions just in case. I usually just add my URL or Link to Screenfly to test. (See link below). Also another thing I do is use % rather than Ratio to adjust image, text, and background settings.  http://quirktools.com/screenfly/

creating a mobile version of a website can be a headache for developers. The smartphone-owning demographic has seen exponential proliferation over the past decade, and that created a need for improved HTML standards. End users want to be able to access a web resource at any time and via any device which makes having responsive websites a requirement. HTML5 has made mobile support a lot simpler by being able to cater to the low-powered electronic devices like tablets and smartphones.

In My Phone TWO Apps is running

If we use bootstrap for developing webapps,bootstrap give responsive nature for these apps.So due to this responsive nature these apps run as native apps in smartphones.

They usually run on webviews, which shows almost like a browser but without some components like browser address fileds.

Is not running as a native application is a web application after all. The new updates for the web like "Web workers" and other technologies give to the web application quite close feel as Native App but still is harder when it comes to the local access on the device, camera, mic, etc etc are easier controlled by the native apps.  

If we use  apache cordova in development we can build same native like applications with ease. We can perform all operations as we can do in native apps.

There are lot of framewokrs available like IONIC, Material UI, Jquery Mobile and others. IONIC is most widley used framework which depends on angular from google. It has beautiful UI components and allow to access native mobile API very easliy. So we can access Camera, Call List, Sms, Location or any native mobile API.

Html5 apps can run as native apps using Web views. Web view can be embedded in view layer of native apps. Web apps can also make use of frameworks like cordova which provides an interface to native layer using JavaScript

They must be run using the underlying OS.

USE OF FRAMEWORKS LIKE CORDOVA WHICH PROVIDES AN INTERFACE TO NATIVE LAYER USING JAVASCRIPT

One of the first decisions you’ll face is which type of app to build. And there is no single, definitive answer.The debate between Native Apps vs Hybrid Apps vs Web Apps is still going, with no clear winner – and all three choices have their benefits.Your choice will depend on a bunch of competing factors, including your budget and your deadline.The aim of this article is to give you a sound understanding of the different types of apps available and to aid your decision as to what technology you should use to build your app.