It's like looking inside a kaleidoscope. The way I see it, every person has their own color of magic—both of ours are blue, by the way, though mine is more greyish and yours is a lighter, less saturated blue. But places have colors as well. Portland's magic is a certain color, Greysol's magic is a certain color, and so on. And if someone helps teach you the magic or grants you the ability to use the magic, then a little bit of their color seeps in as well.

[ based on the way Strange describes it, he finds it intensely beautiful. He's only ever gotten this starstuck about Arabella before. ]

At the same time, spells have their own visible structure and pattern. I can't explain this part very well, it's most likely something you have to see for yourself, but it's how I can try to piece out that someone's casting a shield spell or trying to dispell something.