Hello Hari and welcome to Seven Forums.
Java is a special programming language that has been in use since 1995. A lot of games and websites and programs use Java. If you don't have it on your computer you won't be able to take advantage of the things that were created with Java. More info here: What is Java and why do I need it?
Some computer manufacturers will include Java on any computer they sell. Other manufacturers don't. Since it's a free product anyone can install it at any time so it's no big deal if it's not on your machine. A lot of people wait until they come across something that needs Java and then they install it. That way you know you're getting the most up to date version. And speaking of up to date, because Java is so popular it is a big target for people who write viruses and other malware. So if you want to keep Java on your machine, make sure you keep it updated.
The original Java was written primarily for Internet Explorer. There was no such thing as Chrome, Firefox, Safari, etc. But as these new browsers became more popular, rather than re-writing the entire Java program for each one, the main program was modified for each browser. These modifications were called plug-ins because the user didn't have to do the downloading and installation. The browser did it.
Since you're being asked to install Java in order to download and watch that video, chances are it was not included by the computer manufacturer. But you could open up Control Panel and go to Programs and Features and see if Java is listed. Or you could go to your Start Menu and then All Programs and scroll through the list. I'm betting you won't see Java listed.
Hope this answers some of your questions.