Chapter-1, Sutra15

Patanjali Yogasutra 1.15:

धृष्टानुष्रविकाविषयवितृष्णास्य वशिकारसंज्ञा वैराग्यम्॥१.१५॥

"Lack of craving for the objects known by the senses and described in the scriptures is vairagya or non-attachment. This level of dispassion enables the yogi to gain a high degree of self-mastery; hence it is called vaśīkāra: self-regulating, self-controlling, self-guiding."

When our senses come in contact with sense objects in the external world, it gives rise to thoughts, feelings and impressions in the mind. These modifications fuel desires and cravings for those objects. Through the practice of yoga, one gains mastery over the mind and its thought patterns. One is able to cut off the flow of impressions from the senses to the mind. This weakens the power of desires. When desires no longer dictate one's thoughts and actions, a state of detachment or non-attachment to the fruits of actions arises. This is the true meaning of vairagya.

In the Bhagavad Gita 2.52, Lord Krishna says: 

यदा ते मोहकलिलं बुद्धिर्व्यतितरिष्यति |

तदा गन्तासि निर्वेदं श्रोतव्यस्य श्रुतस्य च ||

"When your intellect crosses the maze of delusion, then you will attain the Supreme State of liberation from doubts." 

Here Lord Krishna indicates that when through practice of discrimination one gains mastery over the modifications of the mind caused by attachment and aversion to sense objects, the intellect is freed from the veil of ignorance and delusion. A similar idea is expressed in this Yoga Sutra verse on vairagya.

The Chhandogya Upanishad 3.14 says: 

यथा पुरुषः पशुभ्यः सर्वभ्यः प्रेत्य न जाति लोभः । एवमेवायमात्मा सर्वभूतात्मा भूतभ्यः प्रेत्य न जाति लोभः ॥

"Just as a man is free from attachment to all animals, so also is the Self free from attachment to all beings." 

Here the Upanishad indicates that the Supreme Self is forever detached and free from any craving or attachment to beings in this world, just as a person is not attached to animals. This highlights the essence of non-attachment or vairagya.