To put it simply, it is like E-Mail for social networking and cloud applications.
The easiest way to understand how that idea applies is to start with some problems in how current social and cloud systems work.
The current crop of social networking services are closed systems being controlled by a few large companies. They are limited in what they can do and how they can be used. A decentralized approach to this would open the door to innovative extensions to the system, enhanced user choice in matters such as privacy, and complete freedom of use and deployment.
OA Social, on the other hand, allows communication between users on any OpenAutonomy server. There is no central authority governing them. Privacy can be ensured by controlling access to trusted content by adding users to your trust list. Highly specialized access control can be applied by using trust groups so that you can have one group that is, for example, for family, one for friends, one for co-workers, etc, and each user will only be able to see the content you posted for that particular group. This differs from some other social networks which use an "all or nothing" approach to trusted access.
Cloud services are very limited and haven't gained much traction because they are all closed systems not offering much in the way of real innovation. There is no ability for these services to cooperate and there is no real ability for anyone other than the service provider to extend their capabilities.
Opening these systems to allow them to interact with each other would allow the user to benefit from the strengths of each and would allow developers to create great new things. In short, freedom and innovation would prevail.
Consider this: If furniture stores worked like cloud storage providers, they would no longer sell furniture but would rent it out to you only when you are using it. However, they would require that you throw out all the existing furniture in your house and replace everything with their rented furniture. Then, from time to time they would discontinue certain things from their catalogue if they weren't popular or profitable enough and you couldn't continue renting them (this is similar to what happened when Google discontinued their "Reader" product).
OpenAutonomy applications are different since they are able to find each other and cooperate to solve larger tasks. For example: you might upload a picture as part of a social post, which is then saved to your OA Storage and you can later use it to change your user picture in OA Details. While each application is designed with a specific task in mind, they can still cooperate with each other (even across different OpenAutonomy servers).
These are clear problems which can be solved by opening up the system and allowing multiple providers to cooperate. OpenAutonomy is a platform for this open cooperation.