Depends on the kind of graduate school.
For PhD programs, research experience and related recommendations matter. For medical school, there is an expected set of pre-med extracurriculars intended to ensure that applicants have an idea of what health care is like and are still interested in it. For MBA programs, work experience and achievements are a big deal.
But the common theme is that the extracurriculars that matter for graduate school are generally those related to the program subject matter.