How about "compete to" instead of "compete about"
to release the best operating systems.
As computers are becoming an increasingly vital need today (this part sounds really weird.)
Good point! It is tough because o number disagreement. You could also to this:
As computers represent an increasingly vital need...----- this way, you are not saying computers (plural) are a need (singular). Instead, they "represent" the need.
Use a question mark when you pose those questions at the end:
what is an operating system? What are some examples of operating systems? Why Mac OS X might be the operating system of the future?
For good organization, start each of the next 3 paragraphs with sentences about each of these 3 questions, in order.