The Marketing department is responsible for planning, organizing, management and control of the marketing function. It is realizing customer needs and then making and promoting a product to the customers. On the other hand, production department is responsible for producing the product. The marketing department comes up with the idea and production department uses its technology and skills to realize that idea into a product.
The main conflict between these two departments is that the production department normally has issues with the design or concept of the product. They usually take the ideas presented by marketing department as useless or very creative. Or often they say that they do not have the required technology to make that product. On the other hand, the marketing department is not satisfied with the way production department has handled their concept.