Long story short, the GPL requires you to grant a license to run the application for any purpose. You can also not add additional constraints to this. The App Store's terms and conditions say that you may only offer the software to be used under the usage terms that Apple gives. These two things are in conflict. Apple generally does not approve apps with a GPL license and most people think it's because of this reason (as far as I know they haven't ever made a comment about it). A few apps have apparently made it through, it seems this has been an error on Apple's part.
IANAL, but my understanding is GPL means any distribution has to come with source upon reasonable request. Apple doesn't have source and thus can't comply with that, and shouldn't distribute the binaries.
LGPL I believe says that the LGPL portion has to user-replaceable. Seems incompatible with code signing enforcement and static linking.
Now, I think a lot of people are probably breaking the letter and spirit of these licenses and publishing to the app store anyway.
Edit: after googling around, it seems this was a popular conversation topic around 2011, and the part being discussed was mostly Apple's TOS rather than above points about the license.
