What I think the Administration building is...

[Whirligig Girl]

I think the administration building will be a building where you can exchange Funds, Science, and Reputation, as well as derive funding or receive information on budget cuts.

When destructible buildings are added, it could be a means of rebuilding and upgrading the facility from a concrete slab launchpad, garage, and communications trailer to a sprawling connection of buildings.

[weeble]

If you look at the science center you'll see that you should be able to unlock tech w/ funds. I thought the idea eventually was so that you could use funds to purchase rep/science points and then use it to unlock stuff. So I think that will probably one of the features. I hope, hate going on a long science mission to get 50 science just to unlock one of the parts I need. It's a huge pain!

I think they might also use it to act as an information hub on how your space agency is doing. Like a building containing records/logs of which Kerbal did what and when. After all they did mention something about working on ways the logs were done.