One significance is The Holy Trinity: God in three persons. Father, Son, and Holy Ghost. That was revealed to the early Church, yet it also passes logical review and historical verification.
Philosophically, it is the three tests to which we expose theories: proposal, prediction, and experiment.
Not being a physicist, I would be hard pressed to say much about its mass-energy significance. However, it bears directly on String theory, and was the basis for M-theory. It has been awhile since I opened the book on quantum chromodynamics.
I'm not much of a scientist either, but we see 3-in-1 with this. We see a family made of a father, mother, and their son. We see a great deal of wisdom in unities.