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An oscillator is something that oscillates. Something that vibrates. See oscillation for more information.

oscillation of a weighted spring
This spring as an example of an oscillator.  [Image source: By Svjo – Own work, CC BY-SA 3.0, https://en.wikipedia.org/wiki/Oscillation. Retrieved May 25, 2018.]
The term “oscillator” has a special meaning in the history of quantum physics. When Max Planck originally developed the concept of the quantum in 1900, the existence of atoms was not fully accepted. But Planck knew that some entity vibrates and emit bands of colored light that can be viewed with spectroscopes. He called these vibrating entities “oscillators.” In fact, Planck’s “oscillators” were atoms.