Please read a more recent post on this here.
The Jain concept of Asharan means that nobody can make us secure or safe. Nobody can protect us.
Asharan Bhavna means thinking that no other individual can provide a refuge. Nothing external can offer the permanent refuge. When death occurs and the soul has to leave the body, there is no one who can save the jiva from this. Wealth, and family, etc., stay behind and you have to face the future by yourself.
Under this reflection, one thinks that he is helpless against death, old age, and disease. The only way he can conquer death and disease is by destroying all his karma. The soul (person) is his own savior, and to achieve the total freedom and enlightenment, one takes refuge to the true path of the religion and to the five benevolent personalities. They are Arihanta, Siddha, Acharya, Upadhyay and Sadhus or monks. The refuge to others is due to delusion, and must be avoided.
This concept is part of the 12 Bhavnas (Reflections or Thoughts). Some people believe that there are 16 Bhavnas. The following explains what the Bhavnas are. (Taken from http://www.fas.harvard.edu/~pluralsm/affiliates/jainism/jainedu/12bhavna.htm)
Jain religion puts a significant emphasis on the thought process of a human being. A person’s behavior and his actions are the reflection of his internal thoughts, day in and day out. It is not the action but intention behind the action results in the accumulation of Karma. Hence, one should be very careful about his thoughts, how he thinks, and the subject matter of his thought.
To make room for pure thoughts, and to drive out the evil ones, Jainism recommends to reflect or meditate the following twelve thoughts or Bhavnas.
The twelve Bhavnas described here are the subject matters of one’s meditation, and how to occupy one’s mind with useful, religious, beneficial, peaceful, harmless, spiritually advancing, karma preventing thoughts. They cover a wide field of teachings of Jainism. They are designed to serve as aids to spiritual progress, produce detachment, and lead the aspirants from the realm of desire to the path of renunciation. They are reflections upon the fundamental facts of life, intended to develop purity of thought and sincerity in the practice of religion.
The reflections are also called Anuprekshas, longings, thoughts, aspirations, or Bhavnas.
Pravin K. Shah
Jain Study Center of North Carolina