Mandala

A mandala (lit, circle) is a spiritual and ritual symbol in Hinduism and Buddhism, representing the universe. In common use, "mandala" has become a generic term for any diagram, chart or geometric pattern that represents the cosmos metaphysically or symbolically; a microcosm of the universe.
In various spiritual traditions, mandalas may be employed for focusing attention of practitioners and adepts, as a spiritual guidance tool, for establishing a sacred space, and as a help to meditation and trance induction.

Hinduism

A yantra is a two- or three-dimensional geometric composition used in sadhanas, puja or meditative rituals. It is considered to represent the abode of the deity. Each yantra is unique and calls the deity into the presence of the practitioner through the elaborate symbolic geometric designs. According to one scholar, "Yantras function as revelatory symbols of cosmic truths and as instructional charts of the spiritual aspect of human experience"
Many situate yantras as central focus points for Hindu tantric practice. Yantras are not representations, but are lived, experiential, nondual realities. As Khanna describes:

Despite its cosmic meanings a yantra is a reality lived. Because of the relationship that exists in the Tantras between the outer world (the macrocosm) and man's inner world (the microcosm), every symbol in a yantra is ambivalently resonant in inner–outer synthesis, and is associated with the subtle body and aspects of human consciousness.

Western psychological interpretations

According to art therapist and mental health counselor Susanne F. Fincher, we owe the re-introduction of mandalas into modern Western thought to Carl Jung, the Swiss psychoanalyst. In his pioneering exploration of the unconscious through his own art making, Jung observed the motif of the circle spontaneously appearing. The circle drawings reflected his inner state at that moment. Familiarity with the philosophical writings of India prompted Jung to adopt the word "mandala" to describe these circle drawings he and his patients made. In his autobiography, Jung wrote:

I sketched every morning in a notebook a small circular drawing, ... which seemed to correspond to my inner situation at the time. ... Only gradually did I discover what the mandala really is: ... the Self, the wholeness of the personality, which if all goes well is harmonious.

— Carl Jung, Memories, Dreams, Reflections, pp. 195–196.

Jung recognized that the urge to make mandalas emerges during moments of intense personal growth. Their appearance indicates a profound re-balancing process is underway in the psyche. The result of the process is a more complex and better integrated personality.

The mandala serves a conservative purpose—namely, to restore a previously existing order. But it also serves the creative purpose of giving expression and form to something that does not yet exist, something new and unique. ... The process is that of the ascending spiral, which grows upward while simultaneously returning again and again to the same point.

— Jungian analyst Marie-Louise von Franz, C. G. Jung: Man and His Symbols, p. 225

Creating mandalas helps stabilize, integrate, and re-order inner life.
According to the psychologist David Fontana, its symbolic nature can help one "to access progressively deeper levels of the unconscious, ultimately assisting the meditator to experience a mystical sense of oneness with the ultimate unity from which the cosmos in all its manifold forms arises."