|Photo credit: G0DeX|
In the Bible, the Hebrew word ot (אוֹת) is generally translated as "sign" or "wonder." These are some places where the word is used:
- the Sabbath (Exodus 31:16-17)
- male circumcision (Genesis 17:11)
- the mark of Cain (Genesis 4:15)
- the rainbow (Genesis 9:12)
- phylacteries (tefillin) (Exodus 13:16)
- the plagues of Egypt (Exodus 7:3, 8:19)
- three miracles that Moses performs before Pharaoh (Exodus 3:12, 4:8)
- the blood on the doorposts for Passover (Exodus 12:13)
What's the common thread here? Some of these are done by G-d and some by humans, so the word ot can't refer only to supernatural activity where humans are passive observers. Furthermore, the burning bush (Exodus 3:1-5) is NOT referred to as a "sign", but rather as a "marvelous sight":
(1) Now Moses, tending the flock of his father-in-law Jethro, the priest of Midian, drove the flock into the wilderness, and came to Horeb, the mountain of G-d. (2) A messenger of G-d appeared to him in a blazing fire out of a bush. He gazed, and there was a bush all aflame, yet the bush was not consumed. (3) Moses said, “I must turn aside to look at this marvelous sight; why doesn’t the bush burn up?” (4) When G-d saw that he had turned aside to look, G-d called to him out of the bush: “Moses! Moses!” He answered, “Here I am.” (5) And [G-d] said, “Do not come closer! Remove your sandals from your feet, for the place on which you stand is holy ground!”
There is an interesting detail in this passage. First we learn of an angel, and a bush ablaze but not affected by the flames. Then Moses marvels at the bush, while not acknowledging the angel at all!
Ramona Lofton (better known as "Sapphire") wrote: “Every blade of grass has its Angel that bends over it and whispers, "Grow, grow."  Perhaps we are surrounded by unseen angels, which would appear if only we knew how to look.
Or as Eden Phillpotts put it: "The universe is full of magical things patiently waiting for our wits to grow sharper." 
Back to the source
Many years ago I was told  that if you want to understand a Hebrew word, you should find the first place that it appears in the Bible. The word ot first appears in the book of Genesis, on the fourth day of creation:
(14) G-d said, “Let there be lights in the expanse of the sky to separate day from night; they shall serve as signs and seasons, and for days and the years; (15) and they shall serve as lights in the expanse of the sky to shine upon the earth.” And it was so.
When the Bible uses the word ot, it doesn't (necessarily) mean that something is outside the normal laws of physics. Like a rainbow or the planets, it could be part of our ordinary day-to-day experience.
As Einstein said, we can see a world where there are no miracles, or where everything is a miracle. Miracles are in the eye of the beholder, if your wits grow sharp enough you can see them everywhere.
Quote from Sapphire: https://www.goodreads.com/quotes/237936-every-blade-of-grass-has-its-angel-that-bends-over
Sapphire attributes this to the Talmud, and the actual quote is from the Midrash, Bereshit Rabbah 10:6
Rabbi Simon said, "There isn't a single herb or spice that doesn't have a constellation in the firmaments that smacks it and tells it to grow."
This was on the Upper West Side of Manhattan, some time between around 2004-2012. I never wrote down the name of the person who told me, so I can't give proper attribution.