A synthesizer with analog-based circuitry. These synthesizers, in general, use analog-style units (oscillators, filters) that are controlled by voltage (like the old modulars, only pre-wired). Analogs are known for having a warm, pleasing sound, compared to most digitals.
Early analogs, such as the Minimoog, are easily called that: they all have what is called discrete circuitry (transistors, resistors, etc. - no integrated circuits). Later synthesizers, however, used other, more compact analog technolgies such as op-amps and linear integrated circuits.
In the early 80s, the terminology began really getting distorted when synthesizers came out with separate sections controlled by digital technology (for things such as patch memory). Often the oscillators themselves would be controlled by some digital circuitry, to help keep the oscillators in tune. Instead of having VCOs (voltage controlled oscillators), they are often referred to as having DCOs (digitally controlled oscillators). And things got complicated even further by having synthesizers that have oscillators driven by short, looped samples, but have analog filters! (These synthesizers are often called "analog hybrids".)