Collaring- what does it mean to you?

For me, personally, it is a deep and serious thing. I only wear my collar to parties and events, and of course when we're together at home. It's a very "obvious" collar, and I don't have the sort of life/job where I can keep it on at other times. To get around that, I have a chain that is pretty much always hidden under clothing, would look merely decorative if a non-kinky person saw it, but which never comes off. It's got the same meaning as a collar would between us.
It is an exhibition of my submissive side, but I am super-selective about who I play with these days, and that side of myself pretty well belongs to Him. I have noticed some confusion among people (guys, mostly) at events - who seem to think it's a general invitation to all and sundry. I even had one grab my leash not too long ago! Sir was sitting right near me, and that guy got straightened out pretty quick.
I do keep in mind that it's more of a "fashion" thing for some people and don't make assumptions about anyone wearing a collar. But a good rule of thumb is never to take it as a sign of someone being available, since for a lot of us it means that submission has been handed over to one particular person, so it's the exact opposite!