The role of Chef de Cuisine or CDC is one that typically only exists in large kitchens. The CDC reports directly to the executive chef and is the chef's eyes and ears in the kitchen ensuring the chef's vision and quality standards are being carried out in their absence.
Since the role of executive chef is a very demanding one often including managing relationships with purveyor, doing media appearances, managing revenue and costs, managing personnel, and generally keeping the place running, CDCs are appointed to manage the food. They will frequently run service from the pass and ensure that plates are going out exactly as the chef would want them to. They oversee that the sous chefs, line cooks, porters, and runners are functioning as a cohesive unit during prep and service. They are essentially god in the flesh when the head chef is absent.
It could also be that the executive chef is in charge of multiple restaurants and the chef de cuisine is, for all intents and purpose, running the show at one of the restaurants.
The role of chef de cuisine is a very demanding one and a rank that likely takes a decade of work to obtain in large restaurants. Translated from the French literally as "chief of the kitchen" they know how the organization should run and are capable of making decisions quickly to avoid emergencies and keep the kitchen from falling behind.
The role of CDC is higher ranking than that of a sous chef. In a restaurant with multiple chefs, the exec will have one chef de cuisine, an executive sous who is in charge of the other sous chefs, and junior and senior sous chefs who manage other portions of the operations.