CodeIgniter 3 through composer?

Thats quite a bit to cover. In brief:

Or can someone please explain to me in simple english the purpose of /public/

These are the files that a HTTP request can access.
So www.mydomain.com/testing/test.html would go to /public/testing folder and look for the file test.html

How to point apache web accessible folder point to /public/ folder?

I don't think you need to do this on local host. When you host your site your hosting provider will tell you it's preferred folder for public files and set up the system to access only this folder publicly by default. It is usually '/public/' but does not have to be.

So which /application/ folder should I put my MVC files etc... ?

In your initial insatall, you will see the welcome page. That tells you where to find the controller for the welcome page and the view for it too. These are the folders to use. Later, when you are more familiar with CI you can set these to be anywhere you choose in the config file, but I would advise leaving that for now as it is.

And when I typed in the search bar url /localhost/ci3/vendor/ the files are also exposed.

Again, you do not have to worry about that on localhost. It is only when you are hosting your site for real that these things are relevant.

You also asked about the BIN folder, it is short for BINARY and executables are stored in there. You will almost certainly not need this.

Hope that helps,

Paul.