The “Responsibility to Protect“, or R2P in U.N.-speak, is a humanitarian principle that aims to stop mass murder, genocide, ethnic cleansing, war crimes and crimes against humanity. It refers initially to the responsibility of states to their own citizens, but in case states can’t or won’t protect their own citizens, other states can step in, respecting the Security Council procedures. However, this is a last resort, especially if the intervention is of a military nature.
The concept is closely linked to, if not indistinguishable from, humanitarian intervention. Often it’s also called the principle of non-indifference, a sarcastic pun on the principle of non-intervention. Some for whom national sovereignty and non-intervention is still the main and overriding rule in international affairs, see R2P as an excuse for Western interference. Noam Chomsky is a notable if unsurprising example. You can read his arguments here. He is joined by a number of governments that risk being a future target.
However, most in the West aren’t jumping the queue to enter into a legal obligation that can force them to undertake expensive and risky interventions in the name of humanity. The fact that these interventions aren’t only expensive and risky but often also without collateral benefits, doesn’t help either. R2P is not yet a legal rule, more a quasi-legal rule. Some legal or quasi-legal texts include the concept. The Constitutive Act of the African Union includes “the right of the Union to intervene in a member state pursuant to a decision of the African Union assembly in respect of grave circumstances, namely: war crimes, genocide and crimes against humanity”. The same is true for the Security Council of the UN. The concept was endorsed unanimously by heads of state during the World Summit of 2005, so it can be argued that the principle is part of international common law (i.e. international law established by coherent and unanimous state practice).