Ignore does four things:
If my character ignores your character (or often, your character's brigade):
1. My ignoring character can't hurt your ignored character (so your character is immune to my character).
2. Your ignored character can't hurt my ignoring character (so my character is immune to your character).
3. My ignoring character is winning if all of your characters in battle are ignored. This means your character(s) always have initiative.
4. While my ignoring character is in battle, no ignored characters can enter battle (excluding the ignored character(s) already in battle, of course).
If the battle ends with your character(s) ignoring all opposing character(s), then you win the battle. However, no character is discarded, everyone just goes back to territory. So it's almost identical to a stalemate, except one side (the ignored side) always has initiative and the other side (the ignoring side) actually wins the battle (and the LS if the ignoring side is Good and it is an RA).
All immune means is that a character's toughness is essentially infinite, and that character cannot be harmed by abilities on characters and enhancements it is immune to.
Some examples:
Eve ignores female Evil Characters. So if she attacks, she can't be blocked by female ECs (they can't enter battle) vs. her. If someone attacks and is blocked by a female EC, and later bands in Eve, the female EC doesn't get kicked out, but she is now losing the battle. If the battle ended, then all characters return to territories, and no one gets discarded, but Eve (and the first Hero) rescue an LS.
Red Dragon is immune to human Heroes. So if I attack with King David, and you block with Red Dragon, then it is a stalemate. This is because your toughness is essentially infinity, and my toughness is higher than your strength. I can play enhancements, but they can't hurt you (unless they interrupt your ability). You can also play enhancements, and if you increase your strength to 11 or higher, then you are winning and I will be discarded if the battle ended.
That's about as simple as it gets. If you have additional questions, feel free to post them here.