"Quality" backlinks are your links from sites with high page ranking. "Garbage" backlink are your links from sites that are no longer in existence. Speaking of backlinks, can somebody tell me how can I have an altavista backlinks? I still can't find answer for this one.
A quality back link is a backlink that links to your site using your keywords, & also appears on a website that has the same or similar content topic as your site... There is a tool called 'backlink builder', I've not used it, but have heard it's good, you enter your keywords, and the builder gives you a list of sites with that keyword,where you can then post articles etc.
"Is it backlinks from high PR sites ? Or do you mean dofollow backlinks ? Or are there some other factors that determine whether a backlink is considered a "quality" one ?" Yes exactly what you meant. Back-links will be validated only if it from a good PR site, whether the content of these two sites are relevant or not. etc etc.
If your site is new, take some time submitting your site to blog directories, make articles in Ezinearticles, Articlebase or Squidoo. But there are free software that can ease the submission of your links to more than 100 directories. Have good relation with other bloggers or website owner in order for you to exchange links.
quality backlinks mean links from high pr, relevant content, do follow. also, article syndication is an effective way to promote your new site.