Angelophany is often a term people use to describe the visible manifestation of angels to mankind, but really should be understood as being the ability to perceive angels with one or more of the five senses.
Angels in both the Hebrew and Christian Bibles often speak to mankind through dreams and visions. For example, many of the ancient prophets found within the same literature recount having great visions of the angelic while being transported unto higher realms of Spirit (heavens). Perhaps, this is why many associate angelophany with only being physical manifestations visible to the human eyes.
Angels typically are described having the form of men. In fact, in ancient literature they are often mistaken for humans, only later to be revealed as possessing great wisdom and might. Sometimes, angels are described as being visible light beings who provide guidance, not unlike what one may read in near death experiences (NDEs). This form of angelophany (the NDE) is quite common.
Angels in various religions may be believed to play a role of intervention, messenger, healer, guide, miracle worker and protector. The role of angels seems to vary dependent upon the situation or the religious belief.
Today, angelophany is not often described as contact through dreams and visions, but is more often understood to be a one-time appearance during times of crisis in a person's life. For example, should a person experience a mysterious visitor who brings help of some sort (See: Mysterious Visitors Angel Stories), later the experience may be realized as being a form of divine intervention. In other words, an angel intervened. Otherwise, visitations by angels are currently not a commonly-held social belief.
Today, most people who claim to be in contact with angels, receive angelic messages through either prayer or meditation. It is more rare for a person to have constant audible contact with the angelic, though some gifted psychic-mediums do possess such an ability.
See: Angel Reader
Also See: Hear Angels?