What on earth is audiation first of all?
A complete description of it can be found at Wikipedia. In essence, it is what many people refer to as, "playing by ear." Playing by ear is a lot of fun, and can dramatically increase how quickly you learn a piece of music. Playing by ear allows you to change from focusing on the logistics of reading the music, to focusing on actually makingmusic. Learning to play by ear, and applying basic Music Theory to what you can hear will allow you to play the basics of most popular music literally within minutes. No need to buy the overpriced book that has your favorite song in it, once you can start to play by ear (of course, applying theory to it in the left hand is an important part of this - that's why it’s one of the core pillars) you will be pleasantly surprised at how quickly you can start to play all types of music. Playing by ear requires study and practice in the same way that Sight-Reading, Improvisation, and Composition do. Contrary to what is sometimes proposed - playing by ear is not a "God-given-gift" that is only bestowed upon a lucky few. It can (and should) be developed and honed in the same way that other musical abilities can.
Playing by ear, or reading music – which is better?
We frequently hear people ask “so is playing by ear better, or being able to read music?” As though somehow they need to be (or even can be) mutually exclusive.
You should learn to do both!
The answer is...you should be able to do both. We have learned from experience that many students have neglected any ability to play by ear (this is also further propagated unfortunately by a well-meaning teacher who has little or no ability to play by ear themselves). Then conversely, many of the “self-taught” students have only sat down and plunked around on the piano until they can figure out the first 4 bars of their favorite song. Both scenarios are obviously missing the point. To share music and be a well-rounded musician, you should be able to Sight Read, Improvise, and play by ear. Rather than be looked at as either-or, they should be taught simultaneously.