Explain "witnessing" to me?

I must have read it a thousand times in the intro to Great Debates: “this is the place for witnessing, if you must”. I cheerfully ignored it until recently when I queried somebody for posting a list of beliefs in GD and somebody else (quite correctly, I presume) pulled me up on this.

Anyway, I assume it is something to do with “bearing witness” in the Christian sense, but people use the word around here (I’ve started to notice it now) in a casual sort of way, as if it was something that happened every day on the way to the supermarket. Is this an American thing? I’d never heard the term before, and no-one has ever approached me and “witnessed”, (as far as I can tell).

My dictionary isn’t much help, just gives conventional definitions.

Thanks

Recently asked, and answered, here.

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Thanks, and apologies for repeat thread