This is one of the easiest categories to mess with in timbre. As with all items in the "timbre" category, this is how the jaw effects the color of your voice, the emotional aspect, and the ease of high and low notes while changing it. There are two sides on the spectrum of jaw options. Open and closed. There are variations within, but I'm going to speak in the two extremes here. MOST of the time, you will be in between.
Singing with your teeth/jaw mostly closed (or even shut entirely) will help low notes to a certain degree, but mostly just muffles the overall sound. This is useful for songs that sit low and quiet as well as for those breathy and emotional love songs. When the teeth are closed the emotional aspect of the sound becomes constricted. If a singer is singing about something happy and sings with their mouth shut it will imply the happiness is secret or internal more than outward. If a singer sings a depressing song with their mouth shut it may be because they want to sound as though they are unwilling to share their feelings. It has its place, but singing with the teeth shut or nearly shut is almost more of an effect and not recommended for standard everyday singing.
Singing with your teeth/jaw open helps bring out high notes. There is an appropriate amount of open your teeth should be, which is two fingers (the taller way) between the front teeth. Any more than that often will create a pinch in the throat and actually hinder your ability to sing. If singing at the top of your range, I recommend getting used to this opening, even if it feels somewhat exaggerated to a beginner. The emotional aspect of an open jaw is the opposite of the closed, you are outward with your feelings. Letting the world or the subject of your song know exactly how you feel.
To expound on the emotional aspect of the jaw, if you were singing a song like "chandelier" by Sia you would most likely begin the song with your teeth mostly shut and pop all the way open for the chorus. The verses are more subdued and internalized while the chorus is the singer partying away to forget the sadness.
The jaw is not very complicated. The most difficult parts are the control of the emotional aspect and acquiring the fully open jaw comfortably and without tension. Opening the jaw to the extent necessary can be tricky and going back and forth within a song can feel somewhat "sock puppety" at first. If you need help, sign up for a singing lesson with me or leave a comment and I'll do my best to help.