I have not been able to find a very early occurrence of “IHS”. There are some (online) who claim that it is to be found in the catacombs, but I have yet to locate a safe affirmation of that.
The most common interpretation is that IHS (or its alternate IHC) is a christogram, based on the first three capital letters of the name of Jesus in Greek, ΙΗΣΟΥΣ (this is semi-Latinised to IHSOVS).
Using C for Σ began in the 4th Century BC, becoming standard in late antiquity and the Middle Ages. Hence IHC from ΙΗϹΟΥϹ.
Alternative interpretations have included
- Jesus Hominum Salvator – Jesus, Saviour of people
- Jesus Hierosolymae Salvator – Jesus, the Saviour of Jerusalem (Hierosolyma).
- In Hoc Signo (In hoc signo vinces) “in this sign you will conquer”, a reference to Constantine’s vision.