Complex sentence: When a transformation, like a rotation in physical space, commutes with the Hamiltonian, the transformation is called a symmetry (behind a degeneracy) of the Hamiltonian − − the Hamiltonian expressed in terms of rotated coordinates is the same as the original Hamiltonian.
Split into simpler sentences: When a transformation, like a rotation in physical space, commutes with the Hamiltonian, the transformation is called a symmetry behind a degeneracy of the Hamiltonian. The Hamiltonian expressed in terms of rotated coordinates is the same as the original Hamiltonian.