“Big ears” means knowing how to listen, and what to listen for.
All the practicing in the world won’t make you a good musician if you don’t develop your listening skills. The best players can play the right thing because the music suggests it. The specific parts each person plays are shaped by the other parts and the overall feel of the music. Everyone is listening and reacting to everyone else, balancing the different elements to create the whole.
Even a soloist playing alone has elements to balance. There is a dynamic flow through the form of the song, and the relationship between melody and accompaniment. A strong rhythm part balances the different parts of the beat the same way a drummer balances the different parts of the kit. These things can all be worked out in a practice session, but each gesture should be executed consciously. We decide what to do and how to do it in the practice room, but in performance we practice the action of executing the thought in real time.
A good listener is a sensitive accompanist, a dynamic soloist, and a good conversationalist. It’s most important skill a musician can have, and the single best way to elevate your playing. Best of all, all you need to do is start paying attention.