how can cordova open app from http or https url?

For the same problem I've used existing webintent plugin, modified the android manifest file - add those lines to activity

<intent-filter>
    <action android:name="android.intent.action.VIEW" />
    <category android:name="android.intent.category.DEFAULT" />
    <category android:name="android.intent.category.BROWSABLE" />
    <data android:host="example.com" android:scheme="http" />
</intent-filter>

and modified the index.html ondeviceready:

function deviceReady() {
    window.plugins.webintent.getUri(function(url) {
        console.log("INTENT URL: " + url);
        //...
    }); 
}

EDIT

I've just noticed a behavior which may be unwanted. When you open the app using the link (intent) from another application, it will (in many cases) create a new instance and not use the already running one (tested with gmail and skype). To prevent this a solution is to change Android Launch mode in config.xml file:

<preference name="AndroidLaunchMode" value="singleTask" />

(It works with cordova 3.5, not sure about the older version)

Then you need to add one more function to ondeviceready:

window.plugins.webintent.onNewIntent(function(url) {
    console.log("INTENT onNewIntent: " + url);
});

This one is triggered when the app was already running and was brought to front with intent.

What you are looking for is called "Universal Links" on iOS and "Deep Linking" on Android.

And there is a Cordova plugin to handle that: https://www.npmjs.com/package/cordova-universal-links-plugin