Certification is official proof that something is true or authentic, or the process of obtaining that proof. To work as a life guard, you need certification in both swimming and first aid — and a whole lot of sunscreen.
If you want to be an elementary school teacher, you'll need to get certification, which shows you've been tested and found qualified to teach. Likewise, an auto mechanic's certification demonstrates her education and skill at car repair. One element of certification is demonstrating your ability, and the other is obtaining a document (or certificate) so you can prove that ability to other people.