Dvesha is an emotional response that negatively influences one's perception of the world. Preferences are born out of one's previous experiences resulting in likes and dislikes. These preferences give rise to judgment that can ultimately affect the ability to reach enlightenment.
Being influenced by aversion can lead to labeling everything as either "good" or "bad." For example, aversion can manifest as believing a certain group people are good while others are bad. This results in a state of disharmony with those who don't share the same views and, in extreme cases, can lead to discrimination and even war.
The best way to address dvesha is to become aware of it's presence in one's own mind. It can be as simple as becoming mindful of one's own personal preferences. Practicing yoga and meditation helps to increase self-awareness and promote the quality of one's thoughts and actions. Consciously begin to observe dvesha and its patterns, its quality and the triggers. Such monitoring of aversion will eventually lead to letting go of it and moving closer to spiritual enlightenment.