I want to transfer files from one folder to another or an entire folder in my web space. I don't want to download it and upload it, can I do this using a PHP script. Please help me. I'm just learning the basics of PHP

If you are using cPanel, you can backup your entire directory and FTP to another server using the Backup utility. Consequently, you can do the same with your database--but you have to download the datbase (which is very small) and restore your database using another server's cPanel Backup utility.

Is this enough or would you like this in PHP?

I was asking about transferring inside my hosting space.
Say from folder,
home/livi/examples to home/examples

I've seen this functionality in some sites.

I'm sorry, I misread the initial post.

Using your cPanel, you can move folder or file(s) to wherever you want. The trick is to practice with one file before moving the whole thing. Click the folder/file you want to move and choose MOVE from FILE MANAGER.

Using your FTP program you can click and drag folder/file from one place to another. Some FTP programs will act just like your Explorer where you can copy and paste to your desired location. This does not mean you have to download to your local drive.

You do not need PHP to transfer files. If you want to though, you can read something from the W3Schools about the PHP filesystem thing.
Using FireFTP or another FTP program of your choice, you can drag and drop folders (even cut and paste for some) wherever you want them in your hosting account's file system. If you don't have FTP software, you can do so in cPanel (it takes longer). Practise with 1 file first and see if it is what you want done.