I wonder if the word has a clear meaning in a food context.
I'm not sure it does, at least in a universally-understood sense. I think it's more one of those "I know it when I see (taste) it" kind of things.
I'll try and use an analogy; it's possible for the same piece of music to be played with the same instruments, and for one version to sound clear, bright, and clean (meaning that each instrument is recognizable and discernible individually AND that all the instruments harmonize and come together well, resulting in an overall experience that's greater than the individually great elements.....while the same piece can be played by the same instruments and the end result can be muddy, unbalanced, and just downright bad.
The same is true of food. A ceviche of snapper, chiles, tomatoes, onion, herbs, and citrus juice can be transcendant, if the individual elements are all high-quality and they're combined skillfully so that they're in balance. But the same dish of the same elements might be a flavorless mush, or muddy, or overly acidic when the ingredients aren't up to par or they're not prepared well.
It's hard to talk about food and flavors using language that is clear and universally agreed-upon, which is why people often co-opt descriptors from other arenas. The language of wine description springs to mind. This whole "bright" thing may fall somewhat into that realm.