Swayambhu is a very important concept in Hindu religion. The meaning of Swayambhu is That which created itself. Numerous murtis (vigraham or bimbams or idols) of gods and goddesses worshipped in Hindu temples are Swayambhu. The term Swayambhu is used for Brahma, Vishnu and Shiva.
That alone was there and then That took a form. This form is Swayambhu. The formless takes a form for the sake of living beings.
Swayambhu also means that which appears not from egg or yoni or womb. In fact all living beings in universe appear from the Swayambhu form. Swayambhu form of Shiva or Vishnu is thus the primordial egg or the source of all animate and inanimate on earth.
Living beings appear when the Swayambhu form of Shiva or Vishnu when they decide to create different kinds of beings.
A cycle of creation comes to an end when the Swayambhu form decides to take back all that appeared from That.
Swayambhu murtis worshipped in temples are that which are not made by human beings or any other living beings. These murtis or idols appeared on its own to bless devotees. The murtis contain the power the particular murti. We have numerous Shivlings, Ganesha, Hanuman, Durga and other murtis which are Swayambhu.
A deity can appear at the same time in many different places. There is no end to swayambhu forms on earth.
Even today many people are blessed with Swayambhu murti or idols of their ishta devata by following dharma and through unwavering devotion. Usually they get the exact location of the murti in dream or they accidently discover during some kind of activity.
There are also swayambhu forms of deities that appear in nature like the famous Amarnath Shivling.