Gradual awakening means that change and healing happen gradually as a result of the accumulation of causes. This is more the common way that healing is understood to occur. As a result of doing this and that a person gradually gets better.
Source: The Psychology of Zen Buddhism (dissertation)
All of you think it's better to be a man than a woman, you think it's better to be a priest than a layperson, and you think it's better to be Japanese than American. But I will always be a woman, and I will always be a layperson, and I will always be an American, and here I am.
The approach to it ( Mind, Absolute, Void, Buddha Nature, Enlightenment ) is called the Gateway of the Stillness beyond all Activity. If you wish to understand, know that a sudden comprehension comes when the mind has been purged of all the clutter of conceptual and discriminatory thought-activity. Those who seek the truth by means of the intellect and learning only get further and further away from it. Not till your thoughts cease all their branching here and there, not till you abandon all thoughts of seeking for something, not till your mind is motionless as wood or stone, will you be on the right road to the Gate.
Source: The Zen Teachings of Huang Po - on the Transmission of Mind - translation by John Blofeld