The attitudes, beliefs and philosophy surrounding the importance of design with regards to product, brand and marketing. It is not relegated only to the design teams but should be cultivated across all product teams that have a role in helping the product succeed in market.
Organizations always have a predominant culture, but within the company there will be several overlapping cultures that guide smaller teams. Much like you can have a culture for a region, a state, and then a city or even suburbs within a city, a design culture is a part of a larger culture but one that the product team must adopt.
The digital product space is highly competitive. A decade ago, simply having a digital solution was enough to create a profitable business. But today those same businesses are competing against many others while consumer standards for user experience and design are higher than ever. Tech companies a decade ago were often engineering-driven, but today they must be design driven. It has to be important to everyone on the product team.
Product managers, designers, developers, QA, customer support, and even marketing and sales have to move fast. They must iterate quickly, respond to customer feedback in-flight, and add in new features collaboratively. By sharing a strong design culture, they can ensure the digital product will maintain high quality without slowing the teams down.