(Just some thoughts, not meant to be comprehensive, barely even coherent)
Incantatory magic to me is an elegant simplicity of words strung together in order to commend oneself to the protection and favor of divinity. The appeal to the spirits is a call to come forth, to guard the petitioner. The words themselves build around the caster as an armor - the words tell a story and, in the telling of it, makes story come to life by mimicking the events in the present time; a sort of microcosm, macrocosm effect. By telling the stories of the spirits (Christian or not), the speaker is viewed literally as calling down the essences, the spirits, of those same stories - seen as very real and independent beings with their own agency and arsenal - to enact upon themselves. Therefore, if the gods hold divine weapons and armor, the petitioner calls upon the gods to loan them the use or power of such instruments of fortitude and protection.
Healing magics by way of incantation weave similar stories to different effect. A charm might tell the story of an injury and how a god or spirit (often a saint) cured it. In this instance, the caster is asking to be loaned the same ability - essentially letting that spirit guide their hands to undertake the healing in the same way that spirit once did. Another form uses the stories of magical items, similar to the lorica (breastplate). The item's story is told and mimicking actions may take place during the recitation to pull on the power of the item itself and its history.
Incantatory storytelling is also used to drive out spirits that may be harmful, banishing them. In this case, the caster uses scenarios in their story that are either "impossible" or hearken to specific realms of spirits, place locations. Either way, it serves the purpose of sending it back or sending it away to a place that either doesn't exist or that cannot be escaped from (the impossibility, the non-existence, creates a perfect trap). By impossibility, it's not just a place that does not exist but also specific scenarios that would never happen. For example, in order for that spirit to be released a condition would need to be met that could never be met. It would be released on a date that would never occur, or under a circumstance that could never happen.
The storytelling aspect of incantation lends history and credence, adding weight to the words. Naming the gods or spirits involved is an immediate way to connect to them, to garner their interest, to appeal for their aid, and to put some of their power to the words being spoken and it's intended effect - if they decide to assist, that is.
"Apportioning" by incantation was used in similar fashion as the method of banishing I've described above, but by driving out the spirit of a sickness or the evil eye using a combination of various locations and repetition. The incantations would describe sending away the illness or spirit causing illness/misfortune to various places - a portion to the mountains, a portion to the rocks, a portion to the hills, a portion to the sea, and so on. By doing this, the purpose was to divide up the affliction or spirit and the "pieces" would be so many and so scattered, the malevolence would have no hope of ever reforming itself.
Symbolism within the words points to the powers ascribed to the being who is called upon for aid. Columkille portrayed as standing astride land and water denotes power over both land and sea. God being referred to as the King of Elements conveys his power as ultimate, dominion over all the elements and therefore, all else that falls under them. Charms calling upon Michael or Patrick evoke their strength, while Brigid and Mary are often called on for healing. Christ's baptism features in several healing charms meant to stop blood flow, and Christ himself is called upon by saints in healing charms - Peter's toothache, and Lucy's eyes. Brigid in particular is called for the protection of cattle and livestock but is also appealed to during childbirth as the midwife of Mary and foster-mother of Christ, and there may even have been a time when Brigid was appealed to as a healer of sight and eye-related injuries. As the spirit's regional folklore grew, so did their repertoire.