What does it mean to say that a language is "effectively closed" under an operation?
"Effectively closed" means that the family is closed under the operation, and that the closure can be computed by giving an automaton/grammar for it (if the original languages are also given in such an effective representation). E.g., given a finite state automaton, we can actually find an automaton for the complement.

Then it is a natural question, whether there are examples of closure properties that are not effective. I know one right now. For a regular language $R$ and any language $L$ the quotient $R/L$ is again regular. There is no effective way to construct a FSA for that quotient if $L$ is e.g. recursively enumarable.