As you probably know, it was not just medieval Christianity that used music for spiritual purposes. As far as we know, music and mysticism have been tied since the beginning of time. But attitudes about what kind of music was acceptable in the church have gone through lots of changes throughout history, and sometimes the specifics are very intriguing.

To answer your question, medieval Christianity is such a broad category that I'd ask you to narrow it down if you can. But generally, medieval Catholicism saw church services for each of the canonical hours, as laid out by St. Benedict in his Rule. Liturgy and monastic lifestyles are not my specific specialty, but if you can imagine attending 8 church services a day (some long, others only 15 minutes or so) and singing in each, going through the entire Psalter (150 Psalms) each week--that was the life!

There are a few reasons why singing is thought to have been so important to liturgical ritual. (There are probably a lot more than I'm going to discuss here, and maybe others will mention them.) One is projection: chanting allowed the words to be easily heard and communicated. One is memory: monks memorized chants instead of reading them as we usually do today (notated music was usually made either to preserve chants or as a memory device, not for sight-reading) and musical settings made words easier to remember. We know today from brain studies that music can connect areas of the brain in unique and holistic ways, and music is now often used in language therapy and to treat memory loss.

And then there's the big one (in my opinion the most interesting): spiritual trance.

Singing with others can induce a trance state and medieval chant was specifically intended to carry the participant into an altered state of mind. Additionally, unmetered chant (having no conductor or necessary leader) operates on the hivemind in which the singers all decide in the moment together how long each not will last and when to move to the next one--they must be very tuned in to one another's sensations and breathing in order to accomplish this together, and it works by subtle instinct. The life of a pious person should be "penetrated by prayer," and people could get high from singing prayers together (still can) in a way that was more profound and connected than speaking them together, or praying silently.

While much of this music today is performed for an audience instead of sung together for its own sake, the only way to experience it as it was intended is to sing it yourself, usually with others. If you can imagine being in a resonant stone chapel and feeling the vibrations and ringing overtones of the humanity around you, and meditating on that in-the-moment experience as it flows through you, that gives you an idea. maybe something like this:https://youtu.be/aySwfcRaOZM or this:https://youtu.be/zUMlhtoGTzY?t=50m32s or a more modern version of a similar concept: https://youtu.be/Wa8cGHlJzqE

If you have the chance to do it--DO IT. And then you will experience it for yourself.