Relevance is the key to high quality backlinks. It makes sense for google to give more weight to links from a relevant domain/page because it’s a much more natural link in the eyes of google. If you were doing link building for your site and google wasn’t in the picture, would you be trying to obtain links from sites that weren’t related to your site? I doubt it.
Having a large number of relevant high page rank pages pointing to your page is the best way to impress google to get some google love. But when obtaining links to your pages, don’t just consider the PR of a page, think about the relevance of the site/page.
The Page Rank system does not consider the relevance of links, and Google looks at various non-PR factors to judge relevance. They use anchor text (the text which is used to link to a webpage) and I suspect that they are also using other types of semantic analysis to determine the link relevance, such as the surrounding text on the page. This is why lower PR pages can outrank higher PR pages.
So when analyzing the competitiveness of a particular keyword, not only do you want to look at the number and quality of links pointing to a page, but also look the anchor text of the links to consider how many relevant links you will need to outrank your competitors.
Even if the #1 page you want to outrank has a lot of links pointing directly to the page, if a lot of the links are not targeting the keyword you are trying to rank for, then its going to be a lot easier ranking for that keyword with fewer quality keyword rich backlinks.
Authority websites like about.com have thousands of links pointing to their site, and hence have many high PR pages, but considering relevance is an important part of the algorithm for ordering websites, if google feels that your page is more relevant for the search query you will outrank the authority site to claim the number one position on google, sending you huge quantities of targeted visitors at the same time.
So don’t get discouraged when a keyword you want to target seems fairly competitive. Obviously it helps when your competitors have weak backlinks, but if there are authority websites in your niche market, a lot of the time these pages are ranking based on domain authority alone but can be beaten.
On further analysis, quite often there isn’t many links pointing to the specific page so there is an opportunity to outrank them if you can get more relevant links to your website.
You will make life easier for yourself if you target the toughest keyword(s) – multiple keywords if they are related – on the home page, which is considered the most important page of a site.