Mentor is a character from Greek mythology whom Odysseus when leaving for the Trojan War placed in charge of his son. A student of a mentor is called a protégé. So now that we have the history and the terminology thing explained, let's get on with the more interesting stuff.
No one is really born with all the knowledge and insight they need in life so we learn from other people around us, sometimes to our benefit or detriment. A good father shows a son how to treat women with love and respect, how to make the right choices in life, how to be strong when life is bad. A good work mentor shows their protégé how to negotiate, or how to sell or how to manage a company or employees. You get the picture.
I feel that "mentor" is a title someone bestows on you, not one you give yourself, unless the protégé tells you that you are/have been a mentor to them. Doing so is just a bit arrogant; some people like to inflate their self-worth by carrying around the label "mentor" when telling stories at work or parties. Not cool. I suspect that I've been a mentor to some, but I'm not seeking out the title or tallying up a protégé list. That's really not important to me. I'm happy trying to just be a good example, not by being perfect ('cause God knows I'm not that), but by trying, failing and learning.
I've been lucky enough to have several mentors. I try to imitate the best from the people I most respect because no one is perfect and totally imitating one person is far too limiting (and a bit creepy). No one person has it all. I don't know where I'd be without some of these key people who have taught me great life lessons, the kind of things you think about when the day gets quiet.
The interesting thing is that we all go through life making an impact on others, perhaps not as strong or formal as a mentorship, but you'd be surprised at how people look at you and think, "that impressed me". It's very humbling when someone starts their story with "I remember when you once said..." I suddenly panic, OMG, what did I say in some flip way or without thinking that has changed this person's view on things. But it usually works out OK, especially as we get a bit older. It's rare that a 20 year-old is a mentor. You've got to give the wine time to mellow a bit.