The Hague Peace Conference of 1899(PDF) proposed that:

"The Contracting Parties agree to abstain from the use of bullets which expand or flatten easily in the human body, such as bullets with a hard envelope which does not entirely cover the core, or is pierced with incisions."

The present Declaration is only binding for the Contracting Powers in the case of a war between two or more of them.

It shall cease to be binding from the time when, in a war between the Contracting Parties, one of the belligerents is joined by a non-Contracting Power.

The treaty was brought about from stories about the damage done to individuals from so called "dumdum" bullets in English rifles:

The so-called ‘dumdum’ bullet, named after the small town near Calcutta where the ammunition factory was located that produced the bullet in the 1890s, expanded on impact, causing disabling wounds and allegedly providing the ‘stopping power’ that British troops felt was necessary to halt advancing ‘brave and fanatical tribes’.

The intention was to prevent horrifying wounds to individuals/soldiers during war.

Generally you get effective prohibitions on weaponry when

a) Both sides feel that, if both sides use it, the weapon just makes the war more horrible without changing the outcome and b) Both sides believe they can easily retaliate in kind if the other guy breaks the treaty.

With hollow points, there's also the somewhat cynical point that, using massed rifles, you would actually prefer to wound your enemy's soldiers rather than kill. A dead soldier isn't shooting at you; but neither (in the usual course of events - the exceptions get medals for extraordinary bravery) is a wounded one, even if the wound is quite light. And a wounded soldier still has to be fed, transported, given medical services.

In Dan Carlin's third episode of the "Blueprint for Armageddon" series he briefly touches on the reasoning behind the Hague Peace Conferences, which were responsible for prohibiting hollow point ammunition in warfare.

His argument is that the Hague Conferences were representative of two trends in European military development at that time: the length of time since the last general European conflict (the Napoleonic Wars), and the huge developments in military science and technology that appeared in the mid to late nineteenth century.

As European militaries began to accumulate new technology, or as technology began to develop which had a clear military use, some politicians and thinkers began to envision what the next general European conflict would look like. These proponents could also turn to colonial conflicts, where dum-dum bullets (expanding rounds) were being used by the British with horrific efficiency in 1899 when the conference was going on. Their conclusion was that one way to prevent such slaughter was to have nations agree not to use certain weapons or exploit materials which could be easily weaponised.

Dan Carlin's interpretation is that this was reflective of a genteel idea of warfare that persisted through the nineteenth century and ended during the First World War. Since most people today would laugh at the idea of prohibiting certain weapons through a multi-national written agreement there may be some truth to it.