Synesthesia is essentially a jumbling of the senses — seeing sounds, tasting colors, that sort of thing.
Language isn't really equipped to fully describe such sensations, but if you've ever taken a large dose of LSD or small dose of anesthesia, you might have temporarily experienced something similar.
I am a synesthete, or "sensory athlete" as I prefer to think of it. For me, synesthesia just is; no drugs required!
The simplest example I can offer is that I "see" certain sounds, usually in the form of a bright flash of light. That high-pitched beeping noise trucks make when backing up causes me to squint.
Harder to describe is what it is like to taste "color". The experience is sort of like what it sounds like, but then again, sort of not. If I'm chomping on something, eyes closed, I "see" color, and "feel" color, and internally assign colorful labels to the flavors, etc., but there isn't necessarily any connection between any of those statements and the actual, literal, visual colors of the food.
Cilantro and parsely are both visually green and happen to also taste greenish too, but that doesn't apply to oregano; its flavor is more tan, like a dirty salt.
With that in mind, when I next say that words have a "taste", what I mean is that words themselves — whether heard, read, or imagined — evoke a sensory-like experience similar to taste, which, for me, means they have both taste-color and taste-texture components.
But no taste-smell. That would be weird.
Grapheme-color synesthesia — experiencing numerals and letters as color — is a relatively common phenomena among synesthetes, though for me the smallest units are words and phrases, not individual characters.
If you've ever waited hours for me to write you a short email, it's because for me, writing is like painting. If I splash words down willynilly, it'll resemble streaks of newborn baby shit. It takes forever to find the right balance of color.
But that's fine. Art does not require speed.