I am not going to offer a dictionary definition. I would have to look it up. I am much too lazy for that.
I am offering the pragmatic definition that comes from 40 years of thinking about logos, of designing logos, of making a logo work in an enterprise's graphic identity system, and of dancing with logos in other design projects.
The best way to think about a logo is as a signature, your signature. Your signature is only yours. Your signature has legal standing. It has gravitas as it triggers awareness with whatever association or relationship one has with the reader.
You sign a letter to your mother, or to a creditor, or your congressman to say this is me. This is what I am saying. This is what I stand for.
Just like your signature, a logo stands in for whatever entity it represents. It says this something exists. This something is the originator or as a participant in some activity or action. This something is credible, has standing.