The IHS is a symbolic monogram of Christ used by the Roman Catholic Church. This monogram consists of the Greek letters iota, eta, and sigma, the first three letters of the name Iesous (Greek for Jesus), the letters of which are also used to spell out the Latin phrase “Iesous Hominem Salvator,” “Jesus, savior of man.” It relates to the story of Constantine, whose vision of the Chi-Rho was recorded by Church Father Eusebius. In the vision, Constantine was reported to have heard a voice proclaim, “In this symbol, thou shalt conquer.” Therefore, the IHS has also stood for “In Hoc Signo,” in this sign. 

The symbol as it appears at right originated in Rome with the early Christians, and was popularized in the fifteenth century by Franciscan disciple Bernardine of Sienna, who promoted it as a symbol of peace.

Some evangelicals have theorized that the initials stand for “Isis, Horus, and Seb,” and are related to Egyptian sun worship, but this is a spurious claim that has never been supported by any solid evidence. Solar and Lunar symbolism have been in continual use by the Church and are most likely continuances of Roman ceremonial symbolism. There is, however, good evidence that the initials were once used to represent Bacchus, the god of wine, who early Christians identified with Jesus. 

The IHS emblem today most commonly represents the communion wafer, and is closely associated with the Jesuit Order. The solar rays often depicted surrounding the emblem represent the monstrance (Ostensorium),* a decorated vessel used to display the Communion Host. The solar symbolism is probably ancient in origin, and probably borrowed from Roman ritual implements.
The three nails pictured on some examples represent the nails of the crucifix.

IHS carving in the Roman catacombs	Another style

*A monstrance or ostensorium is any decorative vessel used to display relics or holy objects, but most often refers to those used to display the consecrated Host.

IHS Monogram