Answer:
A synthesizer uses electronic oscillators (or occasionally digital samples) to create an 'artificial' sound. Many have controls for mixing and modulating this to make unique timbres. Most have keyboards to control them, but rare examples such as the ondes martenot and trautonium use other systems.
Synthesisers can be used to emulate the sound of existing instruments or can be used to make completely new ones. They're very versatile. Modern synthesisers will often have additional sound processing modules such as attack and decay control, distortion or multiple oscillators.
Possibly the most famous synthesizer ever made is the MiniMoog made by Moog, and has featured on countless recordings from classical renditions to abstract rock.