Web App to read data continously from another app
Here's a simple way I'd go about doing it:

Create a backend service that exposes the python script's output via HTTP.  You can use any familiar backend programming language: python, java, .net etc to host a simple http web server, and expose the data.
Create a simple html page, that makes an ajax call to your backend service, pulls the data, and shows it on the page.
Later add your buttons, make the page nicer, responsive on other devices.

Topics to read depends on what you are missing above.  My best guess based on your question is that you are not familar with front end programming.  So read up on html, js, css and ajax.
I have a python script that continuously generates JSON object 
{ time: "timestamp", behaviour: 'random behaviour'} and display it on stdout.
Now I want to build a web app and modify the script so that I can read continous data to my web page. I donno where to start from.
Well in details: I want a web API to have an on/off button and by clicking on it start reading the beahviour and on clicking off it stops. 
I am very new to programming so please suggest me topics and ways I need to study/ look upon to make this app.
thanks