Shilgochu are dried, shredded red peppers (chile threads) used in Korean cooking. The name means "thread" (shil) and "gochu" (chili). These red peppers are most commonly used as a garnish for meat or fish dishes or noodle soups as well as an ingredient in kimchi. They are even used as a garnish on "bindaetteok", popular Korean mung bean pancakes. These chile threads look a lot like saffron threads. Usually the threads are almost fine, hair-like threads. A serving is 2 ounces and about 5 calories.
These are very mild flavored chiles, lightly sweet, with very little heat; again their typical use is for a colorful garnish. They do take on a slightly smoky flavor when toasted. The texture is "chewy" and the flavor slightly salty.
These shredded red peppers can be used anywhere where you want a pop of color. Top a beautiful carrot leek soup or even on a pretty salad. If you're using them to top a soup, try toasting them first in a hot pan just until you can smell the spicy aroma to intensify the flavor. Don't let them burn!
While there is no substitution for the exact flavor; as a garnish you could use safflower threads which are pretty but the color is not quite as vibrant. Safflower threads are easily found in Mexican grocery stores and are less expensive.
Gochugaru would be a good substitute for a similar flavor, about the same amount of heat but probably no easier to find.
Alternately for a little heat and flavor (less sweet) use red pepper flakes or, if you have it, Aleppo pepper.
Of course if you have a Korean grocery store in your area that would be the first place to look for this Korean ingredient. If not, you can purchase them here at Amazon.com. You can find the peppers in little sealed bags or some sources pack them in jars.