Universal jurisdiction is a legal principle whereby states claim the ability to prosecute crimes regardless of where they were committed or who committed them.
Universal jurisdiction is designed to address a fundamental problem with the idea of human rights. Human rights are said to be held by everyone, whatever state they are born into. However, the actual enforcement of these rights is usually carried out by the states themselves. In the UK, if I am robbed, the state will come to my aid and enforce my right to property. But conversely, we find that the greatest violators of human rights are also protected by states themselves; for instance, in Darfur. States like Sudan will plead their sovereignty in defence of their actions, and the advocate of human rights has little recourse. As a matter of practicality, rights follow power.
Universal jurisdiction is hence an attempt to impose a universal concept of rights on a world where, as a practical matter, rights are parochial; it is an attempt to bypass states who would protect violators. But while the criminal prosecution of human rights violations is still carried out at the behest of individual states, it is always open to the charge that it is motivated by the parochial interests of that state rather than loftier principles: hence everything from the Nuremberg Trials to the Hague Tribunal is lambasted as "victor's justice". Which, of course, it is; although this does not make it wrong.
The attempt to forever remove the stain of state interference is hence what motivates human rights advocates to demand universal jurisdiction be exercised by an international body such as the International Criminal Court. But this body would still need to be able to enforce its will on the states, including through violence: rights still follow power.