On & Off Balance
Being 'on balance' and dancing 'off balance' are two very different techniques in ballet. Both have their rightful place and can be exciting showcases on stage.
Soloist dancers often create a huge spectacle with their extraordinary balancing skills. Being still or motionless requires immense control over one's mind and body. Just recall how unsteady you can become when you are nervous.
Famous examples of balancing bravura are the grand pas de deux in act 1 of Sleeping Beauty and act 2 of Don Quixote, Grand Pas Classique to name just a few.
At the opposite end of the stylistic scale is to dance 'off balance', instead of staying put, we may see or experience a suspension or a pendulum-like motion. The neo-classical ballets of George Balanchine may be the most prominent examples of this as well as William Forsyth's masterpiece In The Middle Somewhat Elevated.
Franziska in Balanchine's Tchaikovsky Pas de Deux, 1993
I like to say to my students they should exaggerate their movements so much that they fall from one position into the next. The 'bigger' one moves and the more risks the dancer takes, the more exciting it becomes for the dancer as well as the audience.
If 'being on balance' can be an expression (self) control, power and nobility, 'dancing off balance' can express vitality and energy.
off-balance arabesque, Tchaikovsky Pas de Deux
I believe that before working off balance, students should have a firm understanding of how to balance, which is not about holding a position rigidly but a movement, hence the teacher's request of 'find your balance'. You may like to read more in my article Rigidity in Ballet Class, The Chewing Gum-Theory. It is often underestimated how much control and core strength is necessary to seemingly throw oneself into a position like an arabesque.
However, the old-fashioned claim that the student has to be able to balance (in passé or retiré) before he or she will be able to turn has in my teaching experience not really been the case. Balancing does not automatically translate into the ability to turn.
I have seen students who can stand on one leg without difficulty almost from day one of their ballet training but after years still struggle with pirouettes, their bodies seem 'static', whilst others appear to turn from within even if their physics (e.g. stiff feet and ankles) do not allow a 'correct' relevé (standing on half point or on pointe).