I think this essay offers a good summary of why the Obama administration is appealing the strike down of DADT from a federal state court.

Some key points,

-"Federal courts don't have the power either to enact or to repeal federal statutes. What they have the power to do is declare federal statutes unconstitutional and issue orders prohibiting their enforcement. "

-The ruling of the DADT is bound only to the parties in the case, so only members of the log cabin republicans cannot be subject to DADT policy.

-Without a repeal from congress DADT is still in the books as a policy to uphold, and could be again reinstated by a later administration (if they wanted to)

Here's the fully essay,