Sorry if this question seems stupid. I want to check. What is the importance for getting a high reputation and earning a lot of badges in professional life?
Nobody knows whether or not there will be a miracle in the future --- Joel Spolsky will give you one euro per point you have.
There seems to be some consensus on the main Meta site that mentioning participation on StackOverflow is at best a very minor part of one's resume, reserved for the extra-curricular section. StackOverflow, of course, is a general programming site, and therefore it's possible that participation on the site might be something that an employer might be interested in knowing about.
However, there are few, if any employers who would care about TeX knowledge at all, so participation on the TeX.sx, site is likely to have no use to any potential employer. Additionally, many of us are working academics in various fields and participation in a site like this would have absolutely no bearing on our professional career whatsoever.
I quietly argue in my department and regularly tell colleagues that significant participation in stackexchange sites should count in faculty reviews as service to the scholarly community. I'm sure @egreg's answers here advance science more than does his mathematics, however deep and interesting that may be.
In the professional life probably none. Although, I think badges as professional rewards in Tex serve to signalling what type of scout you are from Wolf Cub Scout to Scout leader. Until you achieve the status of Robert Baden-Powell.