Politics and Democracy
Non-state actors are those who influence global politics, but that are not acting on behalf of states. One example can be terrorists. Sometimes terrorists act on behalf of a state, but more often terrorists claim to be acting in line with an extreme interpretation of a religion.
Non state actors can also include civil society organisations that are not working on behalf of a state (like Amnesty International) or even multinational corporations which might have the HQs in one state, but they are not working for that state, and they might have operations all over the globe.
Non-state actors are generally considered to be a modern phenomenon given multinational corporations, as as we know them today, began to rise towards the end of the 20th century. Likewise, terrorists only really became serious international actors, to the extent that they are serious actors, when global travel and communication became cheap and fast, again towards the end of the 20th century. Civil society grew hugely following WWII as part of the global consensus to make sure no comparable war would happen again.