Your CV (or résumé) details past employment, past education, and any other relevant experience. Ideally it indicates your achievements. All of that is organized so that it is easy for a potential employer to find the information they need to determine if you have the necessary skills and knowledge to do the job they need done.
However, no employer is hiring you for your past. They are hiring you based on an assessment of what you can do for them in the future.
Past activity happens to be the best evidence available on which to base that assessment but no one is under any illusion that it is not flawed. Predicting the future is a notoriously difficult activity.
In your cover letter and in your interview (should you get one), you need to help your potential employer see how all this past activity might translate into future contributions that would benefit the employer.
When you are a typical candidate with a typical background, the person doing the hiring might be able to make assumptions about how your background will play out in the future, based on their own (partial) knowledge of those educational qualifications and former jobs. You probably don’t want to rely on those assumptions. It is always better to do some of this work yourself.
If you are applying for an academic job, say something about where your research program is going next. A tenure-track job leads to a 20 to 30 year career in this department. The hiring committee needs to be able to imagine you as an active researcher throughout that period. Similarly, connect your education and your past teaching experience to concrete contributions to the hiring department’s various academic programs.
If you are applying for a position outside of academia, your particular past is probably atypical of the kind of experience other applicants bring to this employer. You will need to do more work demonstrating how your atypical background will enable you to make a strong contribution. In particular, you need to break down jobs that you understand well but that might not be understood in any detail by the people doing the hiring. If they haven’t done something similar, their knowledge of what a particular job involves is going to be limited. Highlight the relevant elements to help them see the relevance of your experience.
This is not easy. You need to know quite a bit about what the job entails and what the expectations are. This is why information interviews are so important in the job search process. The job ad itself probably doesn’t provide you with enough detail to make a strong case for your potential contribution.
You also have to navigate the tricky terrain between making a strong, plausible case and appearing to be set in your ways and unable to respond to the needs and demands of your potential employer.