Awareness of and acceptance of emotions have been important concepts in psychotherapy since its inception. Freud proposed that unconscious defense mechanisms served to keep distressing and intolerable emotions out of the patient's awareness. The goal of therapy (psychoanalysis at that time) was to help bring these feelings into the patient's conscious awareness.
While it can be useful at times to avoid the experience of emotion (whether by conscious or unconscious methods), a large body of evidence suggests that doing so on a regular basis causes, contributes to, and/or maintains a wide range of mental (and physical) health problems. An increasing number of therapeutic techniques - from DBT to ACT to exposure based therapies - feature acceptance of uncomfortable (and comfortable, of course) emotions and experiences as one of their primary interventions. The irony in this is that acceptance itself and for its own sake is often the goal of these treatments. In fact, accepting negative emotions with the goal of making them go away is not really acceptance at all and is counterproductive. If acceptance of emotions is applied merely as a strategy for getting rid of these emotions then can you really say you are accepting them? Or is part of you engaged in not-accepting (trying to get rid of them)? The very act of identifying ridding oneself of negative emotions as a goal is itself not accepting.
The opposite of acceptance is avoidance. People who cannot or will not accept their internal experiences tend to engage in efforts to avoid them. Examples of avoidance include denial, distraction, repression, and suppression. Drinking or using drugs are also examples of avoidance if they are used in order to decrease the experience of negative emotions or to mask these emotions via their mood-altering effects. People may also avoid situations, places, people, or events that generate distressing emotions.
Avoiding unpleasant internal experiences seems like a common sense goal. After all, who wants to feel unhappy, anxious, or angry? However, if these negative emotions emerge with any frequency a person can end up spending all of his or her time and energy trying to avoid them. Eventually they become so consumed with avoiding that it prevents them from living a meaningful life.
It wasn't until I recognized the role avoidance plays in mental illness that I began to see the relationship between ancient eastern religions (like Buddhism) and modern psychology. Followers of Buddhism have recognized for centuries that mindful, nonjudgmental attention and acceptance of thoughts and feelings reduces suffering and improves the quality and meaning of life. Modern psychology has only started to recognize this over the past 150 years or so. Better late than never, I say.
Even though people have recognized for centuries that avoidance leads to suffering there is little awareness of this in western society in general. We cling fast to the idea that normal = happy and that anything else is wrong and should be corrected.
For me, learning to accept internal experiences has made a radical difference in how I live my life as well as in my work with my patients. I try to pass on what I've learned to others in the hopes that they too will pass it on. The more people who choose to be willing to accept their thoughts and feelings the less suffering there will be in this world.