I did my Ph.D. in mathematics between 2000 and 2007. My first major breakdown occurred in my third year. I thought I'd share some thoughts I had in hindsight.
Ph.D. As An Apprenticeship In Research
Consider an apprentice carpenter. He'll have some basic experience using wood tools at the start. This is like the state of the student once he/she has finished his/her undergraduate degree.
Then there are the tools of the trade of a working academic: reading journals, writing papers, attacking unknown problems.
At Ph.D. level, you have a supervisor, who will set you going with projects, aiming to give you good fertile ground to explore, especially at the start. But as you go on, you start to get more and more used to doing your own research, writing it up, giving presentations on it, attending conferences, and so on.
At the end of the Ph.D., you should be ready to start academic research as a career, perhaps in a postdoc position (as is common with european Ph.D.s), or perhaps straight into a tenure track (as happens with the longer Ph.D. programs they have in the US).
Now just as an apprentice carpenter may have to make some work to show what they've mastered halfway through, so Ph.D. students may be required (as I was) to write a qualifying thesis roughly halfway through to show they could do the full thing. Then, at the end, the student collects the work they've done, turns into a work for examination, just as an apprentice carpenter will show that they've mastered all the skills necessary to start carpentry as a profession.
At the end of a Ph.D., a successful candidate should have mastered the skills necessary, and got their expertise in their area sufficiently good, to start professional academic research. That's the role that an apprenticeship plays in the career of a traditional carpenter/joiner. That's the role that a Ph.D. plays in the career of a researcher: it gets them from where they are at the end of their undergrad degree to the point where they can start working professionally as an academic researcher. Hence the analogy to an apprenticeship.