A Low Frequency Oscillator (LFO) is an important modulation source that produces a repeating signal. The repeating signal will rise and fall as determined by a specified waveform.
Waveforms can vary from simple waveforms (Sine, Triangle, Pulse and Saw) or complex waveforms (Inverted Triangle, Inverted Saw, Ramp, Inverted Ramp, Sample/Hold, Exponential Decay and Inverted Exponential Decay) that can also be designed by the user dependent on the synthesizer being used
This image is taken from the LFO that are available on the Elektron Octatrack
The LFO destination is the sound parameter that is modulating and the most important parameters for programming an LFO are waveform, frequency (rate), destination and amplitude (depth).
When modulating a VCO with an LFO one will hear a vibrato like sound, and when modulating a VCA with an LFO one will hear a tremolo like sound.
LFOs are important for creating complex modulating sounds and have been monumental in the development of many different electronic music styles.
A single or multiple LFOs will be found on almost all modern synthesizers and many different modules providing multiple functions are available.
Its all about modulation!