This depends largely on the tradition that you are coming from. My background is Yoga and from a Yogic point of view a Yantra is part of the tantric tradition; the science of vibration. Yantras are geometrical designs that represent the merging of consciousness and energy and are used in meditation to awaken dormant centres of the brain. For example the Sri Yantra is a visual representation of the sound of OM which is said to be the very first vibration in the universe
Vibrations are still very subtly present in the world today and affect consciousness, energy, mind and matter. In fact everything in nature is affected by sound vibrations. Einstein’s theory that every atom in the universe is made up of vibrations and his famous equation E=mc2 supports this.
The vibrations created while chanting mantras can have very profound effects on the mind and behaviour by subtly calming and focusing the mind.
Yantras are normally made up to triangles and circles within a framework of squares. Square yantras with four doors facing north, south, east and west represent the material world and the inner world of the senses and sense objects. They have four entrances or dwaras (portals) which represent how we function and survive in the material world.
Triangles represent our journey in life. An upward turned triangle represents when consciousness becomes active and our spiritual journey is upwards towards freedom. A downward turned triangle represents a journey towards what is binding, constricting and confining.
An important part of using a yantra for healing is the process of drawing it. A yantra must be meticulously drawn and must be of the exact geometrical proportions to enable the unconscious mind to manifest. Drawing the Sri Yantra is definitely a challenge; you have to concentrate very hard to get the measurements exactly right, but the hard work does focus the mind and when finished gives you a sense of achievement and pleasure.
A Mandala on the other hand is a personal representation of an individual’s inner mind; a subtle link to the higher mind. Creating a personal Mandala can be used to heal and spiritually uplift the mind.