There might be many reasons why the game you've purchased doesn't work with your computer.
All of the technical requirements of the game are listed on the product before you purchase them, so if you know your computer is not compatible then please can you create a support ticket using the link in the top right of this page.
I need more specific information for my game, what do I do?
I suggest you visit this page for Steam game specific help:
https://support.steampowered.com/kb_cat.php?id=19
What can I do, I have a Apple Mac?
Due to the nature of Apple Mac's, their system are very standard and come with the reduce compatibility problems associated with similar desktop/laptop machines.
The only support article Steam provide for Mac's is: How to remove and reinstall Steam on a MAC
What can I do, I have a Windows PC?
The main problem with running a modern game on a Windows computer will be with the Video card.
Either the video card isn't powerful enough, or the software installed in Windows need to be updated. Please select the "Steam, Check for Video Driver Updates" menu in the Steam Client and visit this Steam page for help on updating your Video drivers: https://support.steampowered.com/kb_article.php?ref=6416-EYDH-0477&l=English