To say a person has "regressive tendencies" is a way of saying that the individual being discussed has a tendency to behave in a less mature, or even childish, manner when he or she becomes frustrated or overwhelmed. Regression is a defense mechanism, meaning a way of defending one's psyche.
Someone with regressive tendencies might decide to stay in bed all day where it feels safe when faced with the loss of a job, for example, or might respond with a tantrum when asked to comply with a request.
Everyone employs defense mechanisms to cope with stressors. They are not necessarily unhealthy, as long as they don't interfere with an individual's ability to function adequately. The ideas that led to theories of defense mechanisms originated in the work of Sigmund Freud. Later, his daughter, Anna Freud, took the framework of the psyche her father had developed and fleshed it out by expanding on his ideas and adding her own.
In Sigmund Freud's view, when anxiety arises that threatens to become too overwhelming and cannot be dealt with by taking care of the issue that is causing the anxiety, the mind creates a defense mechanism in order to protect itself. Anna Freud took this concept and expanded it by delineating a total of 10 different defense mechanisms. In addition to regression, the others are denial, displacement, intellectualization, projection, rationalization, reaction formation, repression and sublimation. The list remains intact today, although other defenses have been added to it over time.