The vocal field is competitive, especially in the classical world where many young singers learn similar repertoire. You can get a new piece, glance over it and not read it again until the next lesson if you have a passable voice. But when you take time to practice the song, that puts you ahead of the game. Singers need to work not only on notes, but also on dynamics (whether the music is loud or soft), lyrics and expression. When you sing, you're telling a story. Just as actors practice monologues to deliver them more convincingly, you need to practice your songs to sing them convincingly to your audience. Real vocal professionals can always tell the difference between a singer who knows what she's singing and one who's merely singing the words.
The better you can read music off the page, the sooner you can learn music. You will also learn music independently, without a piano, coach or recording. Aside from practicing your own performance repertoires, you should also spend time looking at scores and music in your chosen genre, partly to familiarize yourself with what's available to sing and partly to improve your sight-reading skills. These skills are very necessary when auditioning for gigs and groups.
Proper breathing and breath control is essential for the vocalist. When you first begin to study singing seriously, you will be taught to breathe in ways you've never thought about. Voice teachers encourage singers to breathe deeply, expanding not only their chests but their stomach muscles and diaphragms. Just as with any other physical activity, these muscles need to be conditioned to function at their best. Only practice can strengthen the singing muscles.
Singers usually start out with a specific register, or range of notes that they can sing comfortably. However, the register is not fixed. A singer can expand his register with practice, especially when he is regularly exercising his vocal cords and breathing apparatus. To expand your own register, you will need to sing near the top and bottom of your register often with a fully warmed-up voice. The greater your register is, the more songs will be available and the more gigs you'll get. True, many singers get by without practice, but if you are serious about your art, you should practice at least two or three hours a day, broken up into hour-long increments to keep your voice from getting tired.