Aristotle defines prohairesis as a desire for things that are up to us to bring about, and it involves both intellect and character. It is not just a wish or a desire, because these can pertain to impossibilities (like immortality) or things not within our control. Prohairesis is always directed towards achievable ends and involves practical wisdom (phronesis).

He distinguishes it from other forms of desire:

• Unlike thumos (spirit or emotional response) and epithumia (appetitive desire), which can be irrational or non-rational, prohairesis involves rational deliberation.
• It is the product of reasoning and thought about what is good or beneficial, typically concerning one's own life and character.

Here’s how Aristotle describes it in "Nicomachean Ethics":
Prohairesis is not concerned with ends (what is to be achieved), but with means to those ends. It is a reasoned and desirable state of capacity to act with regard to human goods.
It is particularly human because it involves reasoning and intellect in a way that simple desire and response do not.

Aristotle's definition underscores the importance of prohairesis in moral action and virtue, making it not just a choice, but a well-considered choice that reflects one's character and values. It is an essential concept for understanding his views on virtue, responsibility, and the good life.