A derivative lawsuit is when shareholders sue on behalf of a company, usually against its own executives or board members. It happens when those in charge make decisions that hurt the company, and shareholders step in to hold them accountable. 
Mismanaged funds (ie. a CEO uses company funds to buy luxury vehicles and vacations for personal use), engaging in fraud (ie. a CEO falsified financial reports to mislead investors), and violating your duties (ie. board members make decisions, ultimately benefiting themselves instead of the company) can all lead to derivative lawsuits. Defendants will typical invoke the business judgement rule as defense against mismanagment claims