To be all ears is to be listening eagerly or paying close attention. If you heard a rumor that school or work might be canceled due to the weather, you'd be all ears for more news.
The phrase all ears used to have an alternate version, "all ear," that isn't used much anymore. Either way, the idea behind this phrase is that you're paying so much attention to what's being said that you feel like you're made up only of ears. You might also use it in a more sarcastic, annoyed way if you are waiting for an explanation or excuse — go ahead and explain why you ate my leftovers, I'm all ears.