This definition comes from the Women's Aid organisation in the UK.
They are organising a Real Man March in the county this month. I have been invited, and if I go I will get a T Shirt saying "I'm a real man", and my wife will get one that says, "I'm a woman who loves a real man"
Here are the key indicators of realness:-

A 'Real Man doesn't hit, abuse or control
A 'Real Man' doesn't hurt anyone he loves
A 'Real Man' makes a difference
I'm Supporting the 'Real Man' Campaign for Women's Aid, standing up to end violence against women and children.

Personally, I'm not at all keen on violence against men either!
Cheers
Dave