An alternative to Jesus Christ. The H is added due to numerous reasons. Some say it stood for Holy, some say it stood for Harold because of, "Our Father, who art in heaven, Harold be thy name". Other theories about the origin of the H. is:
1. H stood for Haploid since Jesus has no human father.
2. It recalls the H in the IHS logo emblazoned on much Christian paraphernalia. IHS dates from the earliest years of Christianity, being an abbreviation of "Jesus" in classical Greek characters. The Greek pronunciation is "Iesous," with the E sound being represented by the character eta, which looks like an H. When the symbol passed to Christian Romans, for whom an H was an H, the unaccountable character eventually became accepted as Jesus's middle initial.
3. H derives from the taunting Latin inscription INRH that was supposedly tacked on the cross by Roman soldiers: Iesus Nazarenus, Rex Hebrei (Jesus the Nazarene, King of the Hebrews). Trouble is, the inscription is usually given as INRI: Iesus Nazarenus, Rex Iudaeorum (J.C., King of the Jews).
Jesus H. Christ is an expression just as "Jesus Christ" Only with an H added in, most likely for humor.
"Jesus H. Christ! My plunger broke!"