The earliest synthesizers made were not made in a self contained unit like the modern day synthesizer is. Each unit, instead, was self-contained in an individual box (a module, hence the term "modular"). Units were available that both created a signal (VCOs, noise generators) and processed a signal (VCF, VCA, etc.). These modules were mounted in large racks and connected to each other with 1/4" cables. Because you patched together connections with these cables, a particular sound was called a "patch"... and the name has stuck with us to this very day.
These modular synthesizers were usually very big, sometimes taking up entire rooms. Compared to the portable keyboard, a modular synthesizer seems like a burden... until you realize that with a modular synthesizer, you are not restricted to one particular path. Modular synthesizers have the greatest freedom in terms of composing patches, and for this reason they are still used in the studios of film composers and studios that require the ability to make new sounds.
The Buchla and Moog modular synthesizers were the earliest to enter the commercial marketplace; although the Buchla technically was the first, the Moog remains the most famous, for two reasons. The first is that the Moog synthesizer got noticed through the enormously popular release of "Switched On Bach" by Wendy Carlos. The second is that the Moog modular synthesizer defined the standard which all analogs use to this very day: All functions of the synthesizer are controlled by a control voltage (CV) of one volt per octave.
Nowadays, a new type of modular synthesizer is emerging: A virtual modular synthesizer. This modular synthesizer allows you to create the sound on a computer, using virtual "patch cords" and "modules" that synthesizer a very similar sound to a modular, without all of the bulk and cables.