Definitions vary, but it usually tends to involve the extensive production of documents, collection of data and deposition of a significant number of individuals.
Black's Law Dictionary (9th ed.) defines it as "[L]itigation involving serveral parties who are separately represented, and usu[ally] involving multifarious factual and legal issues."
Some litigation can easily be called "complex." Examples include the asbestos litigation, the AT&T antitrust litigation, and Brown v. Board of Education.
Classes of potentially complex litigation include: