selection rules
Selection rules are the conditions that decide which transitions between quantum states a given process can drive, and which it cannot. When an atom absorbs or emits light, not every pair of energy levels is connected: some jumps are 'allowed' and happen readily, while others are 'forbidden' and happen rarely or not at all through that mechanism. Selection rules are the simple criteria that sort the two.
At heart these rules come from the transition amplitude vanishing. If the matrix element linking the initial and final states is exactly zero, no transition can occur no matter how long you wait, and the rule that flags such cases is a selection rule. The zeros are not accidents — they follow from deep symmetries and conservation laws, especially the conservation of angular momentum, since the emitted or absorbed photon carries away a fixed unit of spin.
This is why an atom's spectrum shows only certain lines and not every conceivable one: many transitions are quietly forbidden. The word 'forbidden' is a little dramatic, though. Such transitions are merely strongly suppressed under the simplest approximation; through weaker, higher-order processes they can still trickle through, which is why some 'forbidden' lines are faintly visible in stars and nebulae where atoms are left undisturbed for very long times.
For ordinary light absorption, the orbital quantum number must change by one — a consequence of angular-momentum conservation.
'Forbidden' rarely means truly impossible. A transition forbidden in the simplest (electric-dipole) approximation can still occur weakly through higher-order processes, which is how faint forbidden lines appear in low-density astrophysical gas.