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1.
Listening carefully; keenly attentive.

You listen with your ears, so if you are 'all ears' your entire being is listening to someone speak.
I was all ears as Svet told me his exciting story.
by VAKI5 May 10, 2005
 
2.
eager to listen, keenly attentive
When it comes to gossip, those two are all ears.
by Light Joker August 24, 2005