Q: What is the practical application of Advaita Vedanta in everyday life?
A: The conclusion of Advaita Vedanta is: Brahman alone is real; the individual person you think you are is illusory; the essence (true nature) of the illusory person is brahman; therefore, you are brahman.
What is brahman? Immortal, unchanging, limitless, self-existent consciousness. As such, it does not suffer when the body and mind suffer.
So what is the practical application of knowing that you’re brahman? Well, when you’ve realized the truth of Vedanta for yourself (that you are brahman), the illusory world doesn’t suddenly disappear. It continues on just as before.
But the difference is that instead of going about your life riddled with the anxiety caused by believing that you’re the body-mind, you can live your life knowing that no matter what happens to the body-mind, you are always completely okay (because you are really brahman, not the body-mind). When this is clear, you no longer have to rely on the state of the body-mind (or it’s external circumstances) for security and peace of mind. You understand that as brahman, security and peace are your very nature (insofar as you are ever-present, unchanging and undisturbed by the world). Bringing this knowledge to the forefront of your mind when you’re presented with life’s difficulties is the practical “application” of the self-knowledge gained from Advaita Vedanta.
All my best – Vishnudeva