An oscillator is anything that spontaneously oscillates, i.e. modulates (usually as a sine wave in time).

In electronics, this is a circuit that causes an oscillation in the current and voltage, for example the textbook LC or RLC circuit. The idea is that the circuit does this all by itself. You turn on the power and the circuit starts ringing. So, these circuits are used whenever you need to generate a modulated signal, for example to create a radio transmitter.

The spontaneous oscillation is a result of delayed feedback. Think of a microphone being held too close to a speaker (but in that case the delay is acoustic, not electronic)

An optoelectronic oscillator is an oscillator circuit made using optoelectronic components. Usually the amplitude (or phase) of a laser beam is modulated by a voltage signal using an optical modulator. This is a device that uses the electro optic effect in a Non-linear crystal to modulate the polarization which then becomes a modulation of the amplitude when passed through a polarizer. The resulting modulated optical signal is picked up by an optical detector. This turns the optical signal into a voltage which is then fed back into the optical modulator completing the feedback loop. The delay is determined by the distance between the modulator and the detector (usually the length of optical fiber used). The frequency of the oscillation is determined by the length of the feedback delay.

optoelectronic oscillators are often selected because they are less noisy and more stable than the purely electronic alternative.