The title says it all. Is Gregorian Chant merely a style of music, or is there some deeper meaning behind it? Does it serve some special purpose, or have a usage beyond being a form of worshiping God through song?
During the St. Gregory I papacy (590–604) this form of music was collected and codified, and was (and still is) strictly linked to the liturgy.
In this sense, this is not just a style of music, but it goes together with the Mass and the prayer of "The canonical hours", consisting of eight prayer services: Matins, Lauds, Prime, Terce, Sext, None, Vespers, and Compline.
Gregorian Chant purpose was hence to accompaign the liturgy, but the liturgy itself was build together with the chant. In this sense it has a deeper meaning. It's part of the liturgy.
There are the following good links you could view, which give more detail about the chant.
In general, Gregorian Chant is part of the longlasting Church tradition. It is now still commonly used by Order of Saint Benedict and other monastic orders. In this sense you can find a deeper meaning, because it recalls all the monastic tradition ellements: the silence, the prayer of the hearth.. and others.
I hope this answers to your question.