Synthesis is the artificial production of sound. An expansive definition would include all sound-making that does not come from nature or from the human voice, but in common usage the word is usually reserved for electronic modes of sound generation. Synthesis can be described as an alternative to playback of recorded sounds (sampling, for example), and to processing (manipulating sounds in real time).
In the “classical studio era” (roughly, 1950-1965), synthesis was done using electrical equipment originally designed for laboratory use. The mid 1960s saw the appearance of the first synthesizers, which were built expressly for music making. Between about 1985 and 2000, digital synthesizers became predominant, although analog synthesizers still appeal to many musicians.