The word 'personality' comes from the Latin word persona, the mask used by actors in Roman theatre to change their appearance for a role. The audience expected the actor to behave as the mask suggested, even though the actor did not actually possess those qualities personally - which is why, over time, 'personality' came to mean an individual's own characteristic way of responding to other people and to situations, not a mask put on for an occasion.
Because personality covers such a wide range of human behaviour, no single definition fully captures it, but several psychologists have each added a piece: Robert A Baron defined it as 'an individual's unique and relatively stable pattern of behaviour, thoughts and feelings'; Pervin (1993, via Matt Jarvis 2006) described it as the structural and dynamic properties of a person as reflected in characteristic responses to situations; Cattell (1950) said personality is 'that which permits a prediction of what a person will do in a given situation'; Guildford (1959) called it an individual's unique pattern of traits; Allport (1961) defined it as the dynamic organisation within the individual of the psychological systems that determine a person's unique adjustment to their environment; and Eysenck (1953) framed it as the stable organisation of a person's character, temperament, intellect and physique that determines their unique adjustment to the environment.
What ties all of these together is the idea captured in the textbook's own phrase: personality is 'the relatively stable and unique characteristics of an individual across different situations and varied period of time' - stability (it does not change wildly from day to day) AND uniqueness (no two people share the exact same pattern) are both required; a trait that is only stable but not unique, or only occasional and not stable, would not count as a genuine personality characteristic.
In sport, this matters practically: because personality is relatively stable, a coach who understands an athlete's characteristic way of responding to pressure, instruction, or competition can predict and work with that pattern - for example, knowing that an athlete dislikes being commanded but responds well to cooperative coaching lets a coach adapt their own style rather than expecting the athlete to simply change.