Extension, connection and reflection.
Extension in that I've had an interest in knights, swords and medieval armor since I was little. It's one thing to read about it - but another entirely to grasp a small part of that experience by actually wearing armor, fighting in armor, swinging a sword... so it's an extension of one of my primary interests.
Connection in that by wearing the armor, fighting in it, maintaining it, tweaking it, I have a tiny window into a small part of the life that some of my ancestors probably lived. I know at least my surname is of English and Scottish descent, though I haven't traced my specific tree yet. I don't really care the specifics of who it was (blasphemy?), but just to know that it's something they lived and die by ... so it's a connection to a small piece of that.
Reflection in that whether I wear armor or not, I try to act proper and fitting of a knight. I hold doors open for women, I act courteous towards others unless I am given reason not to, and I try to base my character-reflective decisions around what is correct, not just what is easiest. Somewhat like looking in a mirror, I feel the most "me" when I am in harness... so it's a reflection of self that projects the outward appearance that I hold inside.
I don't do viking, I don't do Jedi, I don't do WW1/WW2, I don't do fantasy - this is much more than just a simple "costume" to me.