High rankings on Google and other search engines are the result of
optimized web page content and good incoming links. You need both to get
high search engine rankings.
The number of links alone is not enough to improve your search engine rankings. It is also important that the other websites are related to your website. If the links to your website include your important keywords in the link text, then it's easier to get high rankings for these keywords.
If the links to your site include your keywords, then search engines will think that your website must be relevant for these keywords.