That's a huge question - but in my view it really boils down to four things:
1) A clear sense of the problem they were trying to solve;
2) Crystal clear focus on only the most high-impact things;
3) Relentless pursuit of excellence in execution.
That fourth one mightn't be a popular one to state, but the truth is that there are a lot of companies who try to do 1 through 3, but 4 always comes into play and Google is no different.
Interestingly I took a look at Google just a few weeks ago...
Google has three important things going for it:
1 - a single mission - >91% of revenue is from advertising
2 - dominance (monopoly) - Google has 70% market share for web-search (Microsoft 20%, Yahoo 10%)
3 - Advertising is a huge market that is migrating on-line
Also, by partnering with hardware manufacturers [Samsung, LG etc] it is trying to keep in front of the users and be the entry point of choice. iOS has 43% market share but Android has 49%.
The trajectory is onward and upward!
Happy to throw out some other opinions but that about captures it for me...