In Europe, we judge students based on their work and abilities. How are their grades? Do they have relevant work experience (TA/RA, maybe part-time industry work, etc)? What projects have they done? What courses have they taken? And of course the odd recommendation letter is always a nice bonus.
We expect students to write up a summary of all these things (it's called a resumé) upon which they are to be judged, and further detailed inquiry can then be made during a possible interview process.
However, as I understand it, it seems to be quite different in the USA. Reference letters is all that matters. Be a mediocre student, but have a good friendship with Professor Abstract Algebra? You're as good as made. Be a fantastic student, but be a bit shy or having done most of your work independently of the professors? Tough luck.
I am particularly bemused by so many of the questions on this very site where professors come to talk about awkward situations where they are being forced to write a recommendation letter for some student that they don't even know. Who the heck is Robert James? I lecture to hundreds of students, for Christ's sake!
Or when you in turn get students here asking for questions about how to approach a professor they've spoken very little to all year and ask them to write a recommendation letter.
And yes, I get it. One day, one time, you'll get a fantastic reference letter from a professor who actually knows and has worked with a particular student, and that reference letter will give you a better understanding of the capabilities and experiences of this student. I get that. But that's only part of the whole process here in Europe: That's the bonus I mentioned in my first paragraph, but we don't make it our everything. We realize that some people might get luckier with recommendation letters than others.
So why do Americans put so much weight on recommendation letters?