The hidden orders have no official existence within Asterism. They had their start in the days before the Fall of the Elven Empire as cabals or conspiracies, organised on patterns drawn from more conventional Asterist orders, and are sometimes (though certainly not always) religious in nature and Asterist in belief.
They exist to promote particular philosophies, ways of life or viewpoints which are not currently acceptable or legal in society at large. As long as they are not plotting treason or other crimes, they are technically permitted under the Code of Willing, which is not to say that they don't have an easier time of it when they keep their existence secret.
Some hidden orders exist within an actual Asterist order or other socially sanctioned group (such as a merchant venture or Workers' Co-Op).