Beni-shoga is ginger pickled in plum vineger (ume-zu), the brine produced when making umeboshi (pickled plum). The red color comes from red shiso (perilla) leaves added in the brine. It is often used for yakisoba (fried Japanese noodles), okonomiyaki (savory pancake) and donburi--sweet and salty, a little 'heavy' dishes; the tangy and crispy beni-shoga adds refreshing taste and texture.
My mother would make beni-shoga after she finished making umeboshi. Using the brine from umeboshi-making, she would marinate armful of fresh, young ginger in a big tub. The tub was stored in the storage space outside of our house, and when I was a child it was my job to go get the beni-shoga. As I would open the lid, I was always mesmerized by the color of the brine and the ginger in it—the deep, almost purple, red.
Store-bought beni-shoga, with vivid red color, often has artificial coloring (and additives, too). Plum vinegar is easily available in health food store, making beni-shoga is not complicated at all, and it tastes so much better and ‘real’ when you make it yourself: I recommend you to try it.
In Japan it's usually made with young ginger that is softer and has milder flavor; if it's available, it would be great if you could use it (in that case, you don’t need to peel it). But regular ginger can be used as well, and that's what I use now. —Kyoko Ide