When I was around 12 or 13, this strange thing started happening in my voice. It felt a little awkward and shaky, so I did everything in my power to stabilize it so it could feel normal again. What I didn't realize was that my voice was developing vibrato, and that instead of letting it happen naturally, I was putting it on hold because I had no idea what it was.
Vibrato can start to appear at any age. I've heard 10 year olds with vibrato, and high school seniors without it. With proper air support and a relaxed, tension free phonation, vibrato will usually make its way into the sound, but it's what happens after we start to develop the vibrato that makes all the difference.
Vibrato is a slight fluctuation in both pitch and volume that occurs in a wavelike pattern in healthy voices. A true, natural vibrato should not feel like much, and frankly, won't sound like much inside your own head. You may sense a gentle pulsating feeling near the soft palate, or you may hear a slight waver in the pitch. This is a problem – we, as singers, like to feel and hear what's going on in our voices. In the case of vibrato, many singers will at some point in their development start to "help" the vibrato out. We want to hear the waves of vibrato in our heads the same way we hear vibrato in other singers we listen to. Instead of trusting the natural vibrato, we try to "make" it happen in a stronger way, and in doing so, the airflow can get disrupted and the root of the tongue can start to tighten. In our heads, it will sound great. To everyone else, it can sound thumpy, too slow, too fast, or uneven.
One of my favorite ways to help students with vibrato issues is to have them place a finger gently under the jaw against the base of the tongue. When singing, this area should remain loose. If it starts to tighten, the student will actually feel the base of the tongue bouncing up and down. If this is the case, the student must learn how to relax the base of the tongue, while still maintaining enough air pressure to engage the abdominals and support the tone. I also encourage students to try to "feel" like the vibrato happens above the cheekbones. If a student is feeling vibrato in the throat, then he is most likely tensing the tongue.
Vibrato issues can also occur when a student does not have enough breath support and subglottal air pressure. (Sub=below, glottis=a fancy name for your vocal cords, so subglottal air pressure is what you feel below your vocal cords when you sing.) If there is very little air pressure, the vocal cords will not fully close and the sound will be breathy. If there is a low to medium amount of pressure, the sound might not be breathy, but it may lack resonance and color. If there is too much pressure, the sound will be squeezed and uncomfortable. You are looking for a happy medium – enough to cause a clear, non-airy sound, to engage the abdominals, but not so much pressure that it makes you feel like you are working too hard. Sometimes when the pressure is lacking, the vibrato can become fast and fluttery. In these cases, I work on helping the student achieve optimal air support, making sure the root of the tongue is not "helping," and that the student is always keeping the sound focused by singing with a steady airflow.
If you are interested in a a more technical article on vibrato, I recommend reading this one by Shirlee Emmons.