Ignore (repel) and Immunity are two different abilities.
Ignore (repel) means that you are "walking right past" your opponent neither of you are being harmed by this action, during the time they are ignored they have infanite initative and can play as many enhancements as they want.
Immunity means your immune character cannot be harmed by the abilities of person(s) you are immune to, and giving you infanite defense. If your opponent gets more defense (*/*) than the immune characters offense (*/*) battle becomes a stalemate. This means that whoever played the last enhancements passes initative to the other player, He may then pass it back if he doesn't want to or can't play anything. If both characters don't wish to play anymore enhancements or effect the battle, battle ends and both characters go back to territory.
To defeat a player who is Ignoring (repeling) or immune to you, you need to interrupt it. You can do this by playing any enhancement that either says "Interrupt the Battle" or "Negate all characters / cards in battle" after doing so, you can defeat those characters by beating their defense (*/*) with your offense (*/*) or using an enhancement that removes them from battle (Capture, Discard, Remove from the game).
Repel is old wording, the on newer cards it will be printed as Ignore.