Ok if a website has 10,000 backlinks in google,and another website has 5,000 backlinks,can the 5,000 backlinks rank higher in search engine rankings if it gets MORE traffic than the 10,000 backlinks site? And does the Traffic have to put by people clicking on the google listing on that site OR can the traffic be from anywhere OTHER than google?
Sites that rank higher will get more traffic not the other way around. On any given search results page you will see sites with fewer backlinks outranking sites with more backlinks. It's more to do with the quality of backlinks than quantity. - Michael
Ranking would depend on how the site was optimized. Ranking higher doesn't mean that you will get more traffic. But it also depends on your targeted keywords that ranks higher if the keywords has more searches. It's really important to select the best keywords that can give higher traffic then use the keywords in optimizing your site.
If you had 10,000 backlinks from 10,000 PR0 sites with no traffic, then Google picks up that it's almost useless or even spam. If you have 100 Sites from PR10, 9, 8, 7, 6 pages and the content from these pages is relative to yoru content, then Google will rank you very high.
I was also under the impression site relevance gives the most weight...and Four27pm is right - it's quality over quantity.
For ranking, you should have quality backlinks, not just quantity. For examples, 100 PR backlinks will always be less than 2 PR8 ones.