Is Ear Training Important For A Singer?

"Ear training" is something of a misnomer. You're not really training your ear, you're training your mind to understand the language of music. And yes, it's very, very important for a singer. Ear training is simply part of becoming a good musician and helps you gain a better understanding of pitch, keys, scales, intervals, chords and a lot of other stuff that's going on in music without even having to touch an instrument. In other words, you can get your musicianship up to such a high level that you'll look at sheet music and be able to hear it in your head. At the very least you'll be able to pick out melodies and basic harmonies.