Sri Ramakrishna used to explain what is true renunciation through the following story.
There lived a couple in a village. One day the husband was about to go for a bath and he had his towel on his shoulder. At that time, his wife chided him saying that he was worthless and that in spite of getting old he was still unable to get rid of his habits. She added that the man cannot live even a single day without her and in comparison, their neighbor was a man of great renunciation. Then the husband asked that what the man had done so as to elicit such praise from her. The wife said that the man had sixteen wives and that he was renouncing them one by one whereas her own husband would never be able to renounce anything. Then the husband retorted, “renouncing his wives one by one. The man won’t be able to renounce anything. If a man wants to renounce, does he do it little by little?” The wife smilingly said that the other person was still better than him i.e. her husband. This really roused her husband who said that the wife was silly and that the other person could never renounce his wives, but he would renounce immediately. So saying, he left the place then and there with his towel on his shoulder.
This is called intense renunciation. No sooner the man found out through discrimination what renunciation really meant, he went away in that very condition without trying to settle back his worldly affairs. He did not even look back at his home.
Sri Ramakrishna used to say that he who wants to renounce should possess a tremendous strength of mind. Once a man is possessed of true and intense spirit of renunciation, he does not hesitate even for a moment before taking the final plunge.