  We show that the existence of string order in a given quantum state is
intimately related to the presence of a local symmetry by proving that both
concepts are equivalent within the framework of finitely correlated states.
Once this connection is established, we provide a complete characterization of
local symmetries in these states. The results allow to understand in a
straightforward way many of the properties of string order parameters, like
their robustness/fragility under perturbations and their typical disappearance
beyond strictly one-dimensional lattices. We propose and discuss an alternative
definition, ideally suited for detecting phase transitions, and generalizations
to two and more spatial dimensions.
