for what should I use fn key by default on mac book pro I have fn key in left bottom conner of my macbook pro keyboard. For what purpose does it exist? 

I understand that I can remap it to my needs, but what is its default function?
It swaps the function of the function keys between the OS X function and the actual F1-F12 key. For example, pressing F1 normally will lower the brightness, but pressing fn+F1 will pass an actual F1. You can see these mappings by looking at the icon on the key itself.

This can be swapped in System Preferences → Keyboard so that fn+F1 will lower brightness and F1 will pass an actual F1.



Alternatively you can swap it by running the following Terminal command, then logging out:

defaults write -g com.apple.keyboard.fnState -bool true


Also, fn+fn is used by default to start OS X Dictation.



Perhaps the most common usage though, is using FN+Backspace to get a delete key.



You can learn this by using help from Finder (⌘?), search for "fn" and read the article titled "Use keyboard function keys"