Not sure about other countries, but in the US, there is no country-wide standard for education. Every state and every school district can make up their own guidelines. So the students arriving at any college or university can have very little common education.
For example, during junior year of high school, in my English class, we had weekly in-class writings, weekly quizzes on the works we were reading, short papers due every other week, vocabulary quizzes every other week, and a long 10-15 page paper, typed, due every nine weeks, one of which was a research paper where we had to credit our sources, have a bibliograry, use footnotes, etc. In the school I transferred to for senior year, I did one piece of writing outside of class and that was a simple two page hand-written character study. No vocabulary, very few in-class writings, no research paper. Class time was sometimes given over to reading the material that should have been read for homework. And this was Honors English, supposedly the top level English class the school offered.
Every high school has different requirements--you can graduate with only two years of history or science or math in many of them. So professors have kids who have had US History four years ago in their classes, sitting next to someone who just spent the last year in high school in an AP* history class.
I think the core requirements are a way of making sure that all students graduating from the college have met certain requirements. Since most universities encourage students to take the requirements early in their academic careers, they also ensure that all students have a basic knowledge of these subjects. Most schools have classes that are clearly "English Lit for the non-English major," and "Math for the math-phobic." Sometimes they are even named, "Biology for Humanities Students," or something like that. Classes that expose the students to a range of topics on the subject, but which aren't too in-depth.
When I was teaching Freshman English, I could be pretty certain that most of the students had read at least one play by Shakespeare, but not the same one. They had probably all read one novel by Charles Dickens, and something by Mark Twain. Beyond that, I couldn't make a single assumption about a shared literary experience, other than the texts we were reading in class. While it isn't the only reason for their existence, the core requirements do manage to get most of the students exposed to basic works of literature, basic math skills, a bit of basic history, etc. It helps to level the playing field, so that professors can refer to things not specifically mentioned in their syllabi.
*AP=Advanced Placement class--students passing the class can take an exam to get college credit for the work done.