(A case study was done and there are facts given by Google listed here) -
We're all trying to play the Google game and one of the key factors in it is LINKS.
The amount of links directing to your site is how Google can tell how valuable your site is. It's pretty simple logic -> If customer likes your site -> He links to your site -> Depending on Page Rank quality -> Google determines the outcome and boom. At the last stage, Google uses many functions and complex algorithms in order to determine if the case was a legit process of receiving the link - YOU JUST NEED TO PLAY SMART!
It’s simple, really – the more links you have coming into your site just means that more people are referring you for something your content is delivering them. And that topic is used as anchor text – that's a whole other topic...
Links aren't easy to get – just as people’s referrals aren't easy to get. Google knows this and values the Links factor in considering websites to rank (GREATLY).
Your number of links is a very significant factor in deciding the SERP movement of your site and truth is, if you don't have many links - It means people don't like you - EVEN IF YOUR SITE HAS HIGH QUALITY CONTENT and no one is acknowledging it (by linking for eg), then Google sees no value in you.
You may ask why...
Search engines are PROGRAMMED, they are MACHINES - They can only see what is given to them and stored in there database about your site - and that is the angle in which they view your links. Yes they are Machines but they are VERY complex and can easily catch many sorts of Blackhat way... *cough*
Overall: Higher the links -> More the value in your site-> Google likes you -> Rank higher -> Everyone's happy!
P.S. I've been doing SEO for quite a long time and my main strategy is link building - Many Internet Marketers know that Link Building works but many people thinks it's a hoax simply because they think that after buying links they are set. There is much more to it -> There are companies and software built out there for Link Building, and that wouldn't be the case if there wasn't any initial proof of it working.