Poise is a dynamic view of the way we use our bodies, unlike the term 'posture' which suggests a more fixed position.
The Concise Oxford Dictionary gives the definition of poise as 'Balance, equilibrium, carriage of one's head...' and we talk about being 'poised for action'.
The online FreeDictionary also gives other definitions, including being 'in full control of your faculties' and also being 'self-possessed' which indicates that a balanced mental state is linked to our being in balance physically.
Poise suggests an active fluidity in our body use and as such is a term that is a more helpful concept to include in Alexander lessons, where the process of our movements and the condition of our bodies is something we work with, rather than aiming at being in fixed positions.
If people think about 'posture' they often aim to 'sit and stand up straight' - but this can be unhelpful as people tend to stiffen and often over-arch their backs, so they feel quite uncomfortable after a short time, then give up and collapse into a slump!
However, thinking of being poised so that we balance on our sitting bones or our feet, tends to bring about a gentler re-alignment that can be maintained more comfortably.