A synthesizer is a digital or analog device for creating electric signals which will be interpreted as audio by a speaker or recording device. You are probably used to seeing synthesizers that look a little bit like pianos, with a row of keys mapped to different notes, but this does not have to be the case.
A modular synthesizer is a kind of synthesizer made up of modules. Each module performs a specific function (like creating a sound, filtering a sound, sequencing notes, etc.) and modules can be connected together with wires called patch cables.
At its most basic level, this lets you make your ideal traditional synthesizer – combining the oscillators, filters, and effects that you like with your favorite keyboard. But, the real magic of modular synthesis comes from the idea of modulation. Modules don’t just input and output audio signals, but also control signals called control voltage. Every knob or button on a module – like the cutoff of a filter or the attack of an envelope – can be controlled by other modules in the system, using the same patch cables that carry audio signals. This gives you the power to create any kind of instrument you can imagine just by patching modules together in different configurations.
Your modular synth can be a traditional keyboard-driven voice, or a generative instrument that creates its own non-repeating melodies. It can be a dedicated effects unit that just processes external sound, or a drum machine that plays back samples according to a sequencer. And, it can be all these things by just re-arranging some cables.
Eurorack is just a standard format for modules. All these modules need to fit into a the same case, get their power from the same power supply, and output the same range of voltages so they can talk to each other. There are many different form factors for modular synthesizers, but Eurorack is by far the most popular. Eurorack modules are about 5 inches tall, work off of 12 volt power, and output +/-10v signals. All the modules in this repository are designed for Eurorack, but it shouldn’t be too hard to adapt them to the standard of your choice.
Here are some quick videos that explain modular better than I can: