It means just what it says: the Android permission system does not try to identify transitive requests to use privilege. For instance, if app A asks app B to do something on its behalf, and in response app B asks the underlying OS to do something, then the OS permission checks only take into account that B is requesting, not that the request originated with A and is being performed on A's behalf.
To understand in more detail, I suggest that you read the following papers:
Android Permissions Demystified. Adrienne Porter Felt, Erika Chin, Steve Hanna, Dawn Song, and David Wagner. CCS 2011.
Quire: Lightweight Provenance for Smartphone Operating Systems. Michael Dietz, Shashi Shekhar, Yuliy Pisetsky, Anhei Shu, and Dan S. Wallach. Usenix Security 2011.
Permission Re-Delegation: Attacks and Defenses. Adrienne Porter Felt, Helen Wang, Alex Moshchuk, Steve Hanna, and Erika Chin. Usenix Security 2011.
Wikipedia on the confused deputy problem.
P.S. In the future, when quoting from someone, you might want to provide the source of the quotation.