Magic square or mystical ball

Here is interesting puzzle, which while simple can be impressive for feeble minds:

English variant:

http://mysticalball.com

Russian Variant:

http://www.ugbereg.ru/magic.html

Translated instructions for russian version:

1. think of any two digit number
   
2. subtract from it digits which its made of (for example if you thought of 54 you need to subtract 4 and 5, result will be 45)
3. find that number and its symbol in the table
   
4. think about that symbol
   
5. Click on large big square above the table.

How does it work ? If you want, time yourself the answer is really rather simple.

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Note: Comments may have spoilers! Come up with solution on your own before reading them.