Essentially because the more links you have, and the more quality links you have, then Google views your site as "important" or with valuable content - therefore ranks your site higher in the natural search engines. If your website is on the 1st page of google compared to the 5th, then your website is being promoted substantially more. How many people do you know who continue to search through what google suggests after the 1st page? Not many I bet, because they will search for some other keywords if they cant find what they want, ergo your website will have been overlooked. If you promote it properly then more people will find it, more leads generated and hopefully more sales/customers
I don't think it is a direct way to promote sites. With quality link building campaign, we can make our sites friendly with search engines, and then help our sites gain a higher ranking, and, we can gain more traffic later.
Just simple, when the people and the bots visit your link in the other sites which you used for link building your site gets promotion.
No link building is not way for promoting website but it is just way for generate backlinks for your website so that website get top ranking.
You need to build links across your network that is involved in your niche. You can do it by interacting and contributing on forums and blogs. But ensure you do everything positive rather than spamming or soliciting for your site. Thus you can build reputation that can bring people directly to your site. Remember direct traffic that spreads out from mouth publicity is more valuable than any other means!
Link building will implement the keyword ranking in search engines, so that website get good promotions.
incoming links (backlinks) are the "votes" of other sites toward quality of your site (at least that was the idea before people started to sell them). more links -> more google love -> more incoming search traffic from google