The answer to this question varies from coach to coach. If a coach is "certified," it means they have graduated from a formal course of study.
The certification process for a coach usually takes 1-2 years. It includes theoretical coursework; experiential learning with fellow coaches; a requirement to have a coach as well as to have paid coaching clients; and to submit session work for periodic skill evaluations.
There are, of course, coaches who are not certified who are doing great work. Personally, I wanted the skills, support and community that certification provided and am grateful for the opportunity to have learned from some masterful teachers and peers.
The International Coach Federation (ICF) is a global organization that sets the ethics, competencies and standards for the global industry of coaching. They also accredit coach training programs whose curricula match their standards.
The ICF website is a wonderful resource for learning more about coach training and many other aspects of coaching: www.coachfederation.org