"The Mac OS X Installer makes sure your computer can use the version of Mac OS X you're trying to install." ?

What does it mean "The Mac OS X Installer makes sure your computer can use the version of Mac OS X you're trying to install." ? from http://support.apple.com/kb/HT2956

Which version of Mac OS X are compatible my computer?

Specifically, my problem is the following:

I want to completely erase my startup disk and make a clean Snow Leopard install but I get the message that "Mac OS X cannot be installed on this computer".

Background:

I have a MacBook 13" bought in 2008 (initially) with Mac OS X Leopard version 10.5.2 (or something like this).

Today it runs on Snow Leopard 10.6.8 after an update I did about two years ago. It is up to date to the latest OS X softeware updates, and the startup disk is repaired and veryfied.

SInce i dont have here with me the initial Leopard istallation disks, I borrowed from a friend an install DVD which is Snow Leopard v.10.6.3 for Macbook Pro.

I have read various thing about which could be the reason for that, but i haven't manage to get a clear answer. Is it because the installation disk is not the one shipped with my machine? It it because I run in 10.6.8 and the disk I have here is 10.6.3?Is it because my machine is a macbook and the disk I have here goes with a macbook pro one? Is it something else? I would really appreciate your help.