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 list context is currently not possible this would serve no purpose.