Analog synths create sound by sending waveforms via a circuit board in a multitude of unique shapes. They're usually characterised by a thick, warm sound.
Each of the waveforms - whether it's a sine, square, triangle or saw etc - generate a tone that is different from one another. The sound generated reflects the look of the wave; for example a saw wave is gritty and sharp.
These raw waveforms can then be filtered. This can range from tweaking resonance/cutoff, and shortening or lengthening notes using release, decay, sustain and attack.