It implies that you are completely focused on what the speaker is saying and are ready to absorb everything they have to say.
Here are some examples of how you might use it:
* "Tell me all about your trip! I'm all ears."
* "Go on, I'm all ears."
* "When you're ready to tell me what happened, I'm all ears."
The phrase originates from the idea that someone's ears are their primary way of absorbing information, and by being "all ears," they are actively listening with their whole being.