A beat frequency oscillator or BFO in radio telegraphy, is a dedicated oscillator used to create an audio frequency signal for carrier wave transmissions to make them audible, as they are not broadcast as such. The signal from the BFO is then heterodyned with the intermediate frequency signal to create an audio frequency signal. Wireless telegraphy is the practice of remote writing (see telegraphy) without the wires normally involved in an electrical telegraph. ... Oscillation is the periodic variation, typically in time, of some measure as seen, for example, in a swinging pendulum. ... A carrier wave is a waveform (usually sinusoidal) that is modulated (modified) to represent the information to be transmitted. ... Broadcasting is the distribution of audio and video signals (programs) to a number of recipients (listeners or viewers) that belong to a large group. ... In telecommunications, to heterodyne is to generate new frequencies by mixing two or more signals in a nonlinear device such as a vacuum tube, transistor, or diode mixer. ... The Super Heterodyne receiver (or to give it its full name, The Supersonic Heterodyne Receiver) was invented by Edwin Armstrong in 1918. ...

Example:

A receiver is tuned to a Morse code signal, and the receiver intermediate frequency is = 45000 Hz. That means the dots and dashes [also known as dits and dahs] have become pulses of a 45000 Hz tone, which is inaudible. To make them audible, we need to shift their frequency into the audio range, for instance = 1000 Hz. To do that, the desired frequency shift is = 44000 Hz, and the desired BFO output waveform is . When the signal at frequency is multiplied by that waveform, it shifts the signal to two other frequencies: and . The difference frequency, = 1000 Hz, is also known as the beat frequency. The other frequency, = 89000 Hz, is an inaudible by-product of the mixer. Morse code is a system of representing letters, numbers and punctuation marks by means of a code signal sent intermittently. ... The Super Heterodyne receiver (or to give it its full name, The Supersonic Heterodyne Receiver) was invented by Edwin Armstrong in 1918. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

By varying the BFO frequency around 44000 Hz, the listener can vary the output audio frequency to suit his/her preference.

Also note that beat frequency oscillator is a misnomer, because the beat frequency is produced by the mixer, not the oscillator.