Answer
Krishna describes the development of consciousness as a gradual process. However, there is also an accelerated process available. If a person is fortunate, they come in contact with a pure devotee, a genuine representative of Krishna. This association marks the beginning of the accelerated path of spiritual advancement.
The process begins with sadhu-saṅga (association with devotees), followed by bhajana-kriyā (engaging in devotional activities), and then anartha-nivṛtti (the removal of unwanted habits and impurities).
Ordinarily, the purification of consciousness takes place gradually over many lifetimes. However, through the mercy of saintly association and devotional service, an accelerated path becomes available.
Even though this process is accelerated, purification is still essential. For purification to take place, one must gradually become free from sinful reactions, sinful desires, and all unwanted material tendencies.
The word anartha literally means "that which has no real value." (Artha means valuable or meaningful, while anartha means useless or unwanted.) Our hearts are filled with countless worthless desires for material enjoyment, and these desires must be cleansed.
Krishna's principle in the material world is:
"As you desire, I reciprocate."
If we desire to forget Krishna, He allows us to do so. Therefore, unless our material desires are purified and replaced by the sincere desire to know Krishna and serve Him, spiritual progress remains limited.
This is why the first result of chanting the holy names of Krishna is described as the cleansing of the heart. As one chants sincerely, consciousness becomes purified, and the blazing fire of material desires within the heart is gradually extinguished.
This stage of purification is known as anartha-nivṛtti. The effectiveness of this purification is directly proportional to the intensity of one's desire to become purified.
If one's desire for purification is weak, then progress through anartha-nivṛtti will also be slow. Even though one has accepted the accelerated process of devotional service, advancement depends upon one's sincerity and determination.
It is like sitting in a high-performance car with a powerful engine but never pressing the accelerator. The potential for speed is there, but the vehicle hardly moves.
In fact, we often do something even worse—we keep applying the brakes ourselves. Similarly, although devotional service has the power to elevate us quickly, we hinder our own progress by continuing to hold on to material attachments and desires.
This is why one of the offenses against the holy name is to continue maintaining material attachments even after receiving spiritual knowledge and instructions. If we knowingly continue to cultivate material desires, our purification naturally becomes slower.
Therefore, the essence of anartha-nivṛtti is to sincerely strive to become free from all unwanted material desires and replace them with the pure desire to know and serve Krishna.