When recording engineers and audio researchers started experimenting with recording better sound in the 1950s, they started trying two offshoots of traditional monaural recording: stereo and binaural. Stereo won the dominant role because it offered a three-dimensional sound without special recording techniques or headphones. You could put a stereo record on the turntable, play it and listen anywhere in the room for the basic effect. Binaural became specialized and monaural nearly ceased to exist.
In monaural recordings, you hear the same thing in both ears whether you are listening with headphones or through speakers. Most early recordings were made this way and the technique viable until the 1960s. The first four albums recorded by The Beatles were monaural recordings from which simulated stereo was produced for stereo albums, but it wasn't true stereo. When EMI, the company that produced Beatle albums, released them on compact disc, they originally used the monaural recordings to get a purer sound.
Monaural recordings might be produced with one or more microphones, but the sound is mixed down to one monaural track. Stereo recordings are made by placing at least two microphones and recording them to separate tape tracks. Both tracks have spillover sound from the other, thus creating a three-dimensional effect that is most pronounced in headphones.
Binaural sound is recorded much differently. It uses two microphones about 7 inches apart on either side of a dummy or mannequin head. This technique simulates the distance between a human's ears, plus the deflection and blockage in sound caused by the head. The idea is to record sound and play it back in headphones as near as possible to the way you would hear it live.
Monaural sound always was the easiest to record and reproduce. Because there is no difference between channels, microphone placement is less important. Most low-end hand-held recording devices, movie cameras and video cameras record sound this way. Binaural sound would be impossible to record on such devices.
One way to create binaural sound yourself is to take an old set of headphones and attach microphones were the ear pieces are, then feed the microphone signals into a recording device capable of recording two tracks from two microphones at the same time. You then could play back the recording directly into headphones. This might be a preferred method because one of the other problems with binaural recording is that each person's ears hear sound differently.