The reason why you are seeing 000 (or 0000) repetitively is to assure you that you are embodying your Higher Self. Your Higher Self is your Soul, a connection to the Infinite Creator. Thus, the Infinite Creator is your ultimate guide and knows you intimately.
Thus, when you keep seeing the time 0000 or 000, the significant meaning is that you are one with the Infinite Creator. In this sense, 000 (or 0000) comes as a subtle message to look at the bigger picture of your life and become self-aware that you are a divine being in your greatest gift, the human body. Being self-aware will help you recognize that you are an extension of the Infinite Creator, a piece of the Universal Source.
You will start to understand that everything was created out of the Creator's thoughts or consciousness. With this insight, you realize that everything and everyone you see around you is the Creator wearing a disguise to play a part in the movie of your life.
Hence, the significance of 000 (or 0000) is that you are "God" wearing a temporary disguise and playing a role in your spiritual growth.
To learn more, here is WILLOW SOUL's list of the spiritual meanings of 000 and the reasons why you keep seeing 000 or 0000 everywhere.
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