A Forbidden Line (or Forbidden Mechanism) is a Spectral Line appearing in astronomical bodies that are not reproduced in the lab because labs cannot sufficiently rarefy a sufficient amount of gas to produce observable lines. The lines form from electron orbit transitions that are sufficiently improbable that their Timescale is much longer than that of collisions between atoms that trigger more probable transitions. Thus the phrase Highly Improbable Line would be more descriptive than forbidden line.
In space, a gas cloud can be large as well as thin enough that collisions are significantly less frequent, allowing sufficiently many of these improbable Forbidden Transitions that we can detect them.
The square-bracket form [N II] indicates forbidden transitions by the given species (e.g., "N II" being nitrogen with a State of Ionization of 1, i.e., singly ionized).
Millimeter-wave Intensity Mapping Experiment (mmIME)
Planetary Nebula Luminosity Function (PNLF)
Tomographic Ionized-Carbon Mapping Experiment (TIME)