How backward link help?

Is it true, if i were to have a link from PR5 or PR6 site to PR3 site, it might improve PR of PR3 web site?

If you are trying to improved PR, links from from dofollow high PR would definitely help. But if you want to improved SERP any one way links would help specially links from relevant site.

I think ranking in serp is more important than page rank. so if I get links from non relevent sites, would it help to increase ranking in serp?

It will help your toolbar PR yes, but I don't think just one PR5/6 link to your PR3 site will improve your PR to a 4 or 5 if thats what you mean... I think it's more to do with the accumulation of links you get as opposed to one-hit-wonders.

Google is getting cleverer at analysing the relevancy of links. A backlink from a relevant site will help your rankings more than a non-relevant link. Also, in order to help your rankings it´s key to have the targeted keywords in the anchor text. PR is just a mathematical formula and it doesn´t necessarily help your rankings as much as a relevant link.

You really cannot tell... It was still either of the two(help or not). I think it was better if you just ask "how much help it can give on my site if i get links from non relevant site "

No one knows the exact algo how google weights it. But one thing for sure, just what Google said, the more relevant the better. So we should stick into this.

No it won't. Google sees everything and it doesn't like irrelevant links!

These are links from other web sites linking directly to your web site (inbound). This type of link carries the most link weighting.A link which comes from a web site with similar content scores more points with the search engines