Synthesizer: How Does it Really Work?

I was watching music video which just pop-up on my Facebook feeds. I can’t remember who posted it, but anyways, I was left in awe when I heard and watched the whole video. I was wondering how they come up such beautiful output of the music considering that they recorded it not in a studio.

So I asked my friend who is an expert in music. And he said that there probably using a minimoog voyager electric sythesizer.

As a no-how in music I still have to research online what a synthesizer can do. Of course Wikipedia has the answer and it says:

A synthesizer (often abbreviated as synth, also spelled synthesiser) is an electronic musical instrument that generates electric signals that are converted to sound through instrument amplifiers and loudspeakers or headphones. Synthesizers may either imitate instruments like piano, Hammond organ, flute, vocals; natural sounds like ocean waves, etc.; or generate new electronic timbres. They are often played with a musical keyboard, but they can be controlled via a variety of other input devices, including music sequencers, instrument controllers, fingerboards, guitar synthesizers, wind controllers, and electronic drums. Synthesizers without built-in controllers are often called sound modules, and are controlled via MIDI or CV/Gate using a controller device, often a MIDI keyboard or other controller.

Still not getting it. Apparently I am not music minded. However if I have the opportunity to operate a synthesizer then I will clearly understand how it works.