Individuals of many animal species are said to have a personality. It has been shown that some individuals are bolder than other individuals of the same species, or more sociable or more aggressive. In this paper, we analyse what it means to say that an animal has a personality. We clarify what an animal personality is, that is, its ontology, and how different personality concepts relate to each other, and we examine how personality traits are identified in biological practice. Our analysis shows that biologists often study specific personality traits, such as boldness, sociability or aggressiveness, rather than personalities in general. We claim that personality traits are best understood as dispositions and that they are operationally defined in terms of certain sets of behaviours, which are studied in specific experimental set-ups. Furthermore, we develop an integrative philosophical account that specifies and formalises three criteria for identifying personality traits, which are used in biological practice. For an individual animal to have a personality trait it must, first, behave differently than others. Second, these behavioural differences must be stable over a certain time, and third, they must be consistent in different contexts.