Monophonic is described as music with only one note or voice, so a monophonic synthesizer (like the legendary Minimoog) is only capable of playing one note at a time. This might sound limited, but these synths are capable of huge sounds when used with modulation.
For example, someone singing on their own would be considered monophonic, if a friend starts to sing with them in the same melody, this would still be monophonic. However, if the friend starts to sing a different melody then the sound would no longer be monophonic, but polyphonic.
Early analog synthesizers were monophonic and this was largely due to the complicated internal circuitry that was required to create sound. It was literally a case of not having enough physical space to fit all of the circuitry inside the synth housing.
Monophonic synthesizers do have their advantages, in the right hands, they can be capable of producing bigger sounds than polyphonic synths. Due to the fact that they only process one note at a time, this allows the synth to dedicate all of its power and resources around that note.
You need to bring a different mindset when working with monophonic synthesizers, they can be more complex and thought-provoking but the end result is a lot more rewarding. You are able to focus on one note a time, giving you a lot more control over the final sound.