While links pointing to a particular site are important to good SEO, equally important is the text or words used to create the link itself. To put it simply, a link is good, but a relevant link is much better. So if a company sells widgets, for example, it would be best for SEO if a link pointing to the company site had the text "widget" in it as opposed to some other irrelevant term. The other side of the Search Engine Optimization equation is keywords. Having relevant keywords in the right location and with the right density throughout the website is a very important aspect of optimizing a website for search.
Keywords are really at the core of the search optimization equation, because it is the ultimate goal of the major search engines to do an excellent job of returning highly relevant results to search engine users. So while there are certainly useful things one can do to improve search engine ranking for a certain search term, at the end of the day it comes down to relevance. If a site is relevant and provides a search engine user what they are looking for, then the search engine has done its job. This is the key to "natural" results, and why providing useful relevant quality content will always win at the end of the day in SEO.