Let's say the html file is called as index.html and is located in the asset folder of the app. The following Activity shows how to load it and display the html in the webview.
import android.app.Activity;
import android.os.Bundle;
import android.view.Window;
import android.webkit.WebView;

import com.livrona.learntodraw.pets.R;

public class AboutActivity extends Activity {

     String summary = "";

     @Override
     public void onCreate(Bundle savedInstanceState) {
          this.requestWindowFeature(Window.FEATURE_NO_TITLE);
          super.onCreate(savedInstanceState);
          setContentView(R.layout.about_activity);

          WebView webview = new WebView(this);
          setContentView(webview);
          try {
               InputStream fin = getAssets().open("index.html");
               byte[] buffer = new byte[fin.available()];
               fin.read(buffer);
               fin.close();
               webview.loadData(new String(buffer), "text/html", "UTF-8");
          } catch (IOException e) {
               e.printStackTrace();
          }
     }

}