One way to look at symbols is as an arbitrary abstract representation of a thing. Like the word-symbol "tree" for the beautiful big plant outside my window that cools us down in summer and gives us a bit of shelter in winter.
Another way to look at them is as a visual stand-in/proxy for the thing. Like the cave paintings showing spear heads, stick men, and buffalo as indicative of hunting. Doesn't capture the full energy of the hunt but the imagery of spears, men, and buffalo gets you a lot closer to the hunt than the word "tree" gets you to a tree.
A third way to look at them is as a container for a thing. Like our metaphors and some of the more complex apocalyptic visions, which in their weirdness draw us into a much larger domain than is covered by just the words on the page or the literal language that makes up the imagery. Archetypes might be said to fall in this category. (Please don't take my stopping at three categories to mean that there are ONLY three ways to look at symbols.)
I would say that the concept of "the Christ" is archetypal not just because it has been filled full of meanings, or it transcends cultures and faith traditions, or even because it finds its way into all kinds of literature, but because even in our own scriptures it is used to draw people into a different way of being. There are times when Paul says you "put off the old man" and "put on the new man" -- and that new man is Christ. We enter into His life, and the concept and all associated metaphors draw us into that path. That's one of the things that archetypes do... they're a bit like common roads that people walk in the course of their life-long development, and Carl Jung explored a few of them in his work. So did Joseph Campbell.
If we look at the Christian path in an archetypal way, as well as from other angles, then we can attend more easily to where the beliefs and creeds hit the ground of our experiences and relationships with each other and the world we've been gifted and put in to steward. And so forth.
Looking forward to Avonia's take.