quantization
Picture a staircase versus a ramp. On a ramp you can stop at any height you like; on a staircase you can only stand on a step — never halfway between. Much of the quantum world works like the staircase. A trapped electron cannot have just any energy; it is restricted to certain allowed values with forbidden gaps between them. Quantization is this rule that some quantities in nature come only in fixed, separate amounts rather than a smooth continuous range.
More precisely, quantization means that a physical quantity — most often energy, but also angular momentum and electric charge — can take only discrete values, like rungs on a ladder. For a bound particle this is not an extra assumption; it falls out automatically when you solve the Schrödinger equation, because only certain wave shapes fit neatly into the confining space, much as a guitar string of fixed length can only sound certain notes. The allowed states are labelled by quantum numbers.
The honest qualifier is that not everything is quantized, and quantization becomes invisible when the steps are tiny. A free electron flying through empty space can have any energy. Even for trapped particles, when a system is large the rungs are packed so closely that the staircase looks like a ramp again — which is why we never notice quantization in a swinging pendulum. It shows up sharply only for small, light, confined things like electrons in atoms.
An electron in a hydrogen atom can sit only at energies like −13.6, −3.4, −1.5 electron-volts, and so on — never at −7 eV in between. To move up it must absorb exactly the energy of one gap; to move down it emits exactly that energy as light. The fixed gaps are why each element shows its own set of sharp spectral lines.
Bound electrons climb a staircase of energies, never the ramp between.
The word 'quantum' in everyday speech often means a huge leap, but in physics a quantum is the smallest possible step. A 'quantum leap' is in fact a tiny, indivisible jump — the opposite of the popular meaning.