It appears to be a conventional label that is applied to transitions between the ground state and another energy level (some definitions specify the first excited level) of an atom and is used in all the physical sciences, not just astrophysics.
e.g. He I (58.4 nm) is a transition from $^1$P to the $^1$S ground state.
In fact all atomic/ionic transitions can be considered resonant phenomena, but the term "resonance line" is applied only to these particular types of transition, perhaps because they are usually the strongest lines in the spectrum from that species, since in most cases, the ground state is the most populated. So there is nothing "particularly resonant" about them
A "resonance line" is:
A spectral line caused by an electron jumping between the ground state and the first energy level in an atom or ion. It is the longest-wavelength line produced by a jump to or from the ground state. Because the majority of electrons are in the ground state in many astrophysical environments, and because the energy required to reach the first level is the least needed for any transition, resonance lines are the strongest lines in the spectrum for any given atom or ion.
And here it is used in that context in astrophysics: (Morton 2013)
The tabulation emphasizes resonance lines, i.e., lines whose lower level is the ground state.
Or in Chemistry: From https://goldbook.iupac.org/terms/view/R05341
The radiative decay of an excitation level may proceed to the neutral ground state and would thus occur at the same energy as the corresponding line in the absorption spectrum. Such a line is called a resonance line and the process is called resonance emission.
Or from the Basic Atomic Spectroscopic Handbook:(https://www.nist.gov/pml/basic-atomic-spectroscopic-data-handbook)
The strongest persistent lines usually include one or more resonance lines, i.e., transitions to the ground level or term.