In this case, the primary power of the Wikimedia Foundation Board of Directors is really to administer the funds needed to operate the servers and to hire and fire the staff that runs those servers. There is a whole bunch of other staff doing what I think to be mostly make work projects to spend their donation money.
They gave unto themselves the authority to run roughshod over the editors and to arbitrarily change user privileges as well as to arbitrarily (at their discretion or due to a lawsuit) remove content from the Wikimedia projects (it wasn't even really approved by the community) and they also set up general policies for all of the various projects collectively. Running the server farm sort of helps give them an edge to be able to decide what goes onto those servers, so I suppose their power should be a given in that situation.
Editorial policies on the other hand are usually decided by community consensus and not by the board with often significant pushback when major changes happen without consulting the community. Since they don't hire and fire the actual administration and cleanup of the various wikiprojects or even deal with individual communities in a massive self-destruct mode (it happens from time to time.... that is the job of the stewards and those guys are elected by the community) they really don't deal too much with the actual content nor is there really any CEO like you might find even with other non-profit groups. The various units of Wikipedia report directly to the board, although the chair of the board usually acts in an executive capacity on a more day to day basis if needed.
The board could start locking the servers from write access or do other really stupid things, but that would just fork the projects and send the volunteers elsewhere. It is a sort of uneasy truce between the volunteer leadership and the board with regards to the real power of the board with a general presumption that the board is going to be doing the right thing most of the time even if on occasion they may screw up. In this situation though, the board members really govern a pretty small organization on the whole consisting of just the paid staff of the Wikimedia Foundation and not much else. It is rather prestigious due to the large number of volunteers who contribute to the projects though.