CE is the European standard. You, as a producer, must manufacture goods according to the European standards if you want to sell them in Europe. A CE Certificate is a certificate issued by a third-party testing organization (like GS-TÜV) that your product is made according to the European standards. A CE certificate can be quite costly, depending on the nature of the product. Yes, most industrial products need to be CE-conform, and in case of leather products you may need a veterinary certification.
However, it is not always necessary to have a CE certification. In most cases, it is enough if you make a Declaration of Conformity in which you as producer declare (and take the responsibility) that your products conform to the EU standards (if not, however, you can get into real trouble, especially if your product is not safe). In this case you can ask your client to share the costs of the certification with you (you will include it in your price anyway).
Your client may insist on a CE Certification for product safety purposes, perhaps because they sell to retail chains, which usually require every possible quality certifications for customer protection.
