What are intent-filters in Android?

When you create an implicit intent, the Android system finds the appropriate component to start by comparing the contents of the intent to the intent filters declared in the manifest file of other apps on the device. If the intent matches an intent filter, the system starts that component and delivers it the Intent object. If multiple intent filters are compatible, the system displays a dialog so the user can pick which app to use.

An intent filter is an expression in an app's manifest file that specifies the type of intents that the component would like to receive. For instance, by declaring an intent filter for an activity, you make it possible for other apps to directly start your activity with a certain kind of intent. Likewise, if you do not declare any intent filters for an activity, then it can be started only with an explicit intent.

According: Intents and Intent Filters

When there are multiple activities entries in AndroidManifest.xml, how does android know which activity to start first?

There is no "first". In your case, with your manifest as shown, you will have two icons in your launcher. Whichever one the user taps on is the one that gets launched.

I could not understand intent-filters. Can anyone please explain.

There is quite a bit of documentation on the subject. Please consider reading that, then asking more specific questions.

Also, when you get "application has stopped unexpectedly, try again", use adb logcat, DDMS, or the DDMS perspective in Eclipse to examine the Java stack trace associated with the error.

An intent filter is an expression in an app's manifest file that specifies the type of intents that the component would like to receive.

When you create an implicit intent, the Android system finds the appropriate component to start by comparing the contents of the intent to the intent filters declared in the manifest file of other apps on the device. If the intent matches an intent filter, the system starts that component and delivers it the Intent object.

AndroidManifest.xml

<activity android:name=".HelloWorld"
    android:label="@string/app_name">
    <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:scheme="http" android:host="androidium.org"/>
    </intent-filter>
</activity>

Launch HelloWorld

Intent intent = new Intent (Intent.ACTION_VIEW, Uri.parse("http://androidium.org"));
startActivity(intent);