It's a bit like begging for extra help, or screaming "HELP, PLEASE - WANT LOTS OF RESPONSES TO MY THREAD!"
Just below any given post is some icons, including a little Police-Badge-6-Pointed-Star-Icon.
If you find somebody's post helpful, you can click that icon and send somebody a note ("Thank You") that shows up visually as little green/yellow icons on top right of a member's post, with their location and "status" icon.
Eventually a bunch of collected dark green, light green, yellow cards get full (15) and become a bronze badge. etc.
I think most of us dig the post-count icon/title more than anything. It's all there for fun of hitting new benchmarks as a forum member.
These days... "REP" doesn't really mean anything here on the forums.
It's a pretty tight-knit community and nobody bangs their drum about how much rep they have - which is good.
I don't actually think anybody responds to a thread simply to get the "rep" (points).
People realize that "will rep" basically means "I really want some help & responses with my thread".
(OPs usually still hand out the "rep" - but I honestly don't think anybody really shows up just to get the rep.)
As summary:
If somebody really, really needs help with their thread & wants a lot of responses - adding "will rep" in the title might pull responders in.
Consider it a "grand-fathered" term for drawing responses into a thread.
Personally, I'm also OK with somebody saying NEED HELP (all in caps, that would convey the urgency of it too).
In my books - everybody should be allowed one or two beggings/HELP-cries/"will reps" during a year.
Hope that explains it.