Excellent singing depends on appropriate technique and how you use your voice. It requires the best possible voice training to ensure that you acquire the technique that is best suited to your voice. Such techniques would depend on utilizing a better understanding of breathing and how it influences, not controls, singing. Being able to vocalize well does not mean that you are necessarily ready to handle a song just as well. Therefore, your teacher will train you using different scales and timbres to help you first understand resonance and then use it to create dramatic effect.
Using resonance will help you create powerful sounds, but being able to convert that into melody via lyrics is a steep order for the not yet completely trained singer. Remember the singing which affects the listener the most is the kind where notes blend into each other to create imagery via sound. This is why many teachers prefer to train their students by using lyrics when practicing scales or different combinations of basic notes. Most important is that your singing should sound effortless — not that you have not put any effort into the singing, rather that the result of the effort more than the effort itself should be perceptible.
This is why experienced voice coaches allow their students to experiment with various styles to ensure that inherent flaws of technique can be identified and rectified accordingly. It is the unhindered expression of emotions which raises vocal music above instrumental music and gives it that defining touch which is so hard to replicate. No two people will express exactly the same range of emotions even if they are singing the same song. This is because perceptions vary and so do interpretations of words and the mood of certain arrangements of notes.
When you are just setting out on your musical journey, you can find voice training tedious. It is up to your vocal coach to decide which levels and styles would be most appropriate for your voice. You might want to sing pop, rock, urban, dance, music theatre or opera. Yet, there are certain limitations imposed by vocal quality which should be recognized at the outset to minimize disappointments. Some teachers do say rather recklessly that anybody can sing. The bottom line is whether people would be willing to listen to that singing. It will be a mix of the quality of voice training as much as your individual hard work and skill which will decide the outcome.