Getting your PhD at a prestigious university, doing a postdoc at a prestigious university, publishing in fancy prestigious journals, etc.?
In an ideal world, the prestige(tm) of your alma mater doesn't matter. As a researcher, you will be evaluated by the quality of your research output.
But it turns out that the world is not ideal. In the real world, there are plenty of situations in which a researcher will be evaluated by people who can't look at the papers of the respective person in detail and make a fair judgement:
- Hiring committees for academic positions
- Companies hiring people "out of academia"
- Panels in funding agencies
Especially when comparing different researchers to whom grants or jobs may be given, it is normally unrealistic to compare their research works in total. There is no time for this, and probably nobody is qualified for a real comparison if the candidates are not exactly from the same niche of a sub-field.
And in these cases, prestige matters. Being affiliated with a good university (or one that is perceived as such) can get you through initial screening rounds, and since the selection processes for positions at these good institutions are often quite competitive, being affiliated with a very prestigious university can give you a subconscious head-start in the heads of the selection committee members. Given that these processes are extremely noisy and often many candidates compete for the same position, such a head-start is highly valuable.
We have an evolved basis for status pursuit. The persons with higher status attract mates more reliably, and the attracted mates tend to have higher status. It works both for men seeking women and women seeking men. This has direct impact on the reproductive success of the persons with status, and on their offspring who share in the penumbra of the higher status. It is effective in many cultural contexts, and even transfers between many cultures. Here are just three items I found in a quick Google search.
So, to put it in colourful terms: Status is important because people with high status get all the girls.
Or rather, our ancestors with high status got all the high status girls. So, any genetic predisposition and any cultural tendency to seek or gain status was reinforced by reproductive success.
If your potential employer judges you on the quality of the university where you got your PhD rather than the content of your PhD (e.g. papers), that is a bit of an indictment of them (lazy academic snobbery). I'm not sure I'd want to work for them because I would want to work somewhere that my skills were actually useful and of interest.
Of course, if the PhD is not necessary for the job, then this isn't so much of an issue.