state declares a lexically scoped variable, just like my. However, those variables will never be reinitialized, contrary to lexical variables that are reinitialized each time their enclosing block is entered. See "Persistent Private Variables" in perlsub for details.
If more than one variable is listed, the list must be placed in parentheses. With a parenthesised list, undef can be used as a dummy placeholder. However, since initialization of state variables in such lists is currently not possible this would serve no purpose.
state is available only if the "state" feature is enabled or if it is prefixed with CORE::. The "state" feature is enabled automatically with a use v5.10 (or higher) declaration in the current scope.