According to Wikipedia, data governance is the discipline that embodies a convergence of data quality, data management, data policies, business process management and risk management surrounding the handling of data in an organization. 
What is the need for data governance?
In simple words, it is required to support the essence of a DW/BI system - presenting a single version of the truth.
The above image shows the process stages of data governance. “A data governance initiative must build competencies, assign roles and responsibilities and invest in technologies to enable these core processes no matter the scope and scale of your business objectives”. 
Let us get into the nitty-gritty of data governance.
Inconsistencies in dimension names and meanings: Reaching a common agreement on the names and meanings of dimensions across an organization having multiple OLTP systems and data marts is a big challenge. In an organization, it is common to have the same keywords, terms and codes meaning different things, or different terms meaning the same thing. For example, a ‘customer’ can refer to individuals in one data mart and organizations in another. The currency notation used in three different data marts (of three departments) can be ‘USD’, ‘US Dollars’ and ‘$’. All of these represent the same currency - US Dollars. Such inconsistencies lead to data quality issues which can have a direct impact on the organization’s revenue.
Begin with conforming dimensions: Conforming dimensions is not an easy task - getting senior managers from different areas of business to agree upon same dimension names, meanings and values especially in today’s ‘agile’ world definitely sounds like a task cut out! What is to be noted here is that everyone need not agree on having the same name for every attribute of every dimension table. Only the important dimensions such as customer, date, product category, etc. need to be identified and conformed. If nothing else, this will reduce the business user’s reconciliation effort and aid in making timely and effective decisions.
Do it NOW: Implementing data governance right away can have a great positive impact on an organization. Delaying the implementation can have many ill effects. For example, as the organization grows in size, it becomes more difficult to get people adjusted to the new data governance policies and standards. Also, if existing issues related to data governance re-occur in the future, the resource consumption for handling such issues increases, thus decreasing the profit margin.
By implementing the data governance business function, the DW/BI systems will provide consistent solutions, help the organization in improving efficiency of developing and implementing new products/features and provide a competitive advantage to the organization by converting the integrated enterprise-wide data to a strategic asset. 
 The Data Warehouse Toolkit, 3rd Edition - by Ralph Kimball & Margy Ross