What are the origins of international humanitarian law?

To answer this question we have to ask other questions.

What law governed armed conflicts prior to the advent of contemporary humanitarian law?

First there were unwritten rules based on customs that regulated armed conflicts. Then bilateral treaties (cartels) drafted in varying degrees of detail gradually came into force. The belligerents sometimes ratified them after the fighting was over. There were also regulations which States issued to their troops. The law then applicable in armed conflicts was thus limited in both time and space in that it was valid for only one battle or specific conflict. The rules also varied depending on the period, place, morals and civilization.

Who were the precursors of contemporary humanitarian law?

Two men played an essential role in its creation: Henry Dunant and Guillaume- Henri Dufour . Dunant formulated the idea in A Memory of Solferino, published in 1862. On the strength of his own experience of war, General Dufour lost no time in lending his active moral support, notably by chairing the 1864 Diplomatic Conference.

Dunant:
"On certain special occasions, as, for example, when princes of the military art belonging to different nationalities meet (...) would it not be desirable that they should take advantage of this sort of congress to formulate some international principle, sanctioned by a Convention and inviolate in character, which, once agreed upon and ratified, might constitute the basis for societies for the relief of the wounded in the different European countries?"

Dufour (to Dunant):
"We need to see, through examples as vivid as those you have reported, what the glory of the battlefield produces in terms of torture and tears."

How did the idea become a reality?

The Swiss government, at the prompting of the five founding members of the ICRC, convened the 1864 Diplomatic Conference, which was attended by 16 States who adopted the Geneva Convention for the amelioration of the condition of the wounded in armies in the field.

What innovations did that Convention bring about?

The 1864 Geneva Convention laid the foundations for contemporary humanitarian law. It was chiefly characterized by:

standing written rules of universal scope to protect the victims of conflicts;
its multilateral nature, open to all States;
the obligation to extend care without discrimination to wounded and sick military personnel;
respect for and marking of medical personnel, transports and equipment using an emblem (red cross on a white background).

Humanitarian law prior to its codification

It would be a mistake to claim that the founding of the Red Cross in 1863, or the adoption of the first Geneva Convention in 1864, marked the starting point of international humanitarian law as we know it today. Just as there is no society of any sort that does not have its own set of rules, so there has never been a war that did not have some vague or precise rules covering the outbreak and end of hostilities, as well as how they are conducted.

Taken as a whole, the war practices of primitive peoples illustrate various types of international rules of war known at the present time: rules distinguishing types of enemies; rules determining the circumstances, formalities and authority for beginning and ending war; rules describing limitations of persons, time, place and methods of its conduct; and even rules outlawing war altogether. (Quincy Wright)

The first laws of war were proclaimed by major civilizations several millennia before our era: I establish these laws to prevent the strong from oppressing the weak. (Hammurabi, King of Babylon)

Many ancient texts such as the Mahabharata, the Bible and the Koran contain rules advocating respect for the adversary. For instance, the Viqayet a text written towards the end of the 13th century, at the height of the period in which the Arabs ruled Spain contains a veritable code for warfare. The 1864 Convention, in the form of a multilateral treaty, therefore codified and strengthened ancient, fragmentary and scattered laws and customs of war protecting the wounded and those caring for them.

The Lieber Code

From the beginning of warfare to the advent of contemporary humanitarian law, over 500 cartels, codes of conduct, covenants and other texts designed to regulate hostilities have been recorded. They include the Lieber Code, which came into force in April 1863 and is important in that it marked the first attempt to codify the existing laws and customs of war. Unlike the first Geneva Convention (adopted a year later), however, the Code did not have the status of a treaty as it was intended solely for Union soldiers fighting in the American Civil War.