An oscillator, in brief is something that oscillates, as per Webster's definition of oscillate:
1.a : to swing backward and forward like a pendulum b : to move or travel back and forth between two points
2 : to vary between opposing beliefs, feelings, or theories
3 : to vary above and below a mean value

In my experience, however, it most often refers to some sort of electronic signal generator. The signal might be a square wave, sine wave, triangle wave, or other periodic signal. There are many ways to make an oscillator, such as crystals or the 555 chip and its relatives. In many cases, the oscillator involves the charging and discharging of capacitors to produce a given voltage. Alternately, with a PIC chip or other microprocessor, one might just twiddle an output bit. This will directly produce square and rectangular waves, and with other components to produce waveform deformations, other waveforms may be produced.

Electronic oscillators are used for many things:

• Clock signals, such as the ones inside your computer and in your digital clocks
• Modulation and Demodulation of a signal, particularly one transmitted via radio waves
• Sound generation, as in sound cards and synthesizers
• AC circuit testing

Sources: A recent Merriam Webster's Dictionary along with the electrical engineering classes I took in college.

Os"cil*la`tor (?), n.

One that oscillates; specif.:

(a) (Elec.)

Any device for producing electric oscillations; esp., an apparatus for generating electric waves in a system of wireless telegraphy.

(b) (Mech.)

An instrument for measuring rigidity by the torsional oscillations of a weighted wire.

 

© Webster 1913