Greetings in that Divine and Most Precious Name of Our Lord and Savior Jesus Christ!
Jah is an English attempt at a transliteration of the Hebrew "Yah" which itself is said to be a shortened form of "Yahweh" though in truth this word "Yahweh" may never have existed in the time of the Hebrew scriptures, Yahweh is an attempt and trying to form an English pronunciation of the unpronounceable name of God in Hebrew, which the copyists chose to replace variously with "LORD" in the Scriptures.
In the Olde English many of the "y"s of other languages were transposed to "j"s and so "Yah" became "Jah" (or "Jahoviah") just as "Ieyesus Kiristos" became "Jesus Christ" its just the particular way original English pronounces these "y" sounds.
In the Rastafari culture, to ascribe the title of "Jah" has several intertwined layers of meanings, on the surface view when applied to HIM Haile Selassie pre-Coronation title and name of Ras Tafari it is to ascribe in various ways the divinity in connection with the Davidic Monarchy. For some, HIM is considered the very incarnation of the Father, for some HIM is the return of Jesus Christ on the Earth, for others HIM is considered an entirely different deity altogether from Western Christianity based on an abhorrence to the histories of slavery and colonialism. For folks like myself, the title of Jah Rastafari is to connect the Divine Godhead which cooperates in Grace through the Divine Theocratic Monarchy of the Solomonic Emperors of Ethiopia. As the Revised Constitution of 1955 elaborated, "By virtue of His Imperial Blood, as well as by the anointing which He has received, the person of the Emperor is sacred, His dignity is inviolable and His Powers indisputable. He is consequently entitled to all the honors due to Him in accordance with tradition." Those folks like myself then do not necessarily believe that HIM is God of himself, rather that God operates THROUGH the personality of HIM as a living saint, similar to the theology of Holy See of Saint Peter and the Vicar of Christ teachings of the Papacy. I know folks will jump on the "this is not Orthodox" bandwagon but I can only testify and witness to you what Rastafari culture is.
There are other levels of the title "Jah" for example other Rastafari brothers, generally Elders or at least folks who serve as community leaders, are also titled "Jah" as in "Jah Pidow" or my good friend "Jah Faith" etc etc.. In this context, the title is meant to acknowledge that God cooperates within human persons, and that God dwells inside the hearts of those we meet, and so to call them "Jah" attached to their names is not to say that each of these are God of themselves, rather that our God is ever-present in those folks we meet and know. In this sense also, I use the title "Jah Rasfafari" for the Emperor as I also call my friend "Jah Faith" not because they are God so much as with God.
When folks then chant "Jah, Rasfafari" it is not necessarily then to "worship" the Emperor, but then to worship God who acts in all our lives at every level. It is to affirm that Jah, the Creator, the Father, was there is Ras Tafari just as he is there with Jah Faith just as he is here with me.