Since this question is located in the topic of business, learning organizations are companies that seek to utilize their human resources to think, plan, reform, and think outside the box to gain a competitive edge in an ever changing world. This is a very broad definition, because there is no set way learning organizations operate. It really is an amorphous field.
With that stated, there are consulting companies that aid companies achieve their goals in strategic ways, but individual companies also have their own internal learning organizations in place.
The benefits of such an organization can be tremendous. Perhaps the best way to get ahead in any industry is knowledge. The more knowledge that you have and the more you are able to use it to gain an edge, the more profitable a company will be.