Short answers, pulled from the story.
An injunction is an equitable remedy in the form of a court order compelling a party to do something or to refrain from doing something. A party that fails to comply may face fines, imprisonment, or contempt of court charges. Its origins trace to Roman law and the equitable remedy of the interdict, and it was developed by the English courts of equity.
A mandatory injunction requires a party to take a specific action, such as cleaning up an oil spill or removing a spite fence. A prohibitory injunction prevents a party from engaging in specific conduct, such as using an illegally obtained trade secret. Many injunctions are both mandatory and prohibitory, requiring certain conduct while forbidding other conduct in the same order.
A super-injunction is an injunction in England and Wales whose existence and details may not legally be reported, in addition to prohibiting disclosure of the underlying facts or allegations. The term was coined by former Guardian editor Alan Rusbridger in September 2009 in connection with a Trafigura injunction that blocked reporting on the 2006 Ivory Coast toxic waste dump scandal. Lord Neuberger's report found that only two genuine super-injunctions had been granted since January 2010.
The Supreme Court set out the four-factor test in eBay Inc. v. MercExchange, L.L.C. A court must find that the plaintiff suffered irreparable injury, that legal remedies are inadequate, that the balance of hardships favors the plaintiff, and that the public interest would not be harmed by the injunction. All four factors must be satisfied before a permanent injunction is granted.
Congress passed the Norris-LaGuardia Act in 1932 in response to federal courts' extensive use of injunctions to break strikes and ban union organizing activity. The Act imposed procedural and substantive limits so extensive that it effectively prohibited federal courts from issuing injunctions in cases arising out of labor disputes. A number of states enacted similar Little Norris-LaGuardia Acts restricting their own courts.
A structural injunction places a court in the position of taking over and administering an institution such as a school, a prison, or a hospital in order to ensure compliance with a legal requirement. Federal courts used structural injunctions to carry out the command of Brown v. Board of Education, at times assuming management of public schools to enforce desegregation.