Often referred to as synth, a synthesizer is a type of electronic musical instrument that produces certain signals that can be recreated as sounds. A synth offers you the possibility of imitating a lot of instruments, from a piano which it resembles somehow, to stringed instruments, flutes, or even the human voice or natural sounds such as wind or waves.
A synthesizer is usually used with a keyboard, but it can be coupled with other instruments too. Of course, the keyboard makes it easier to use. Fingerboards, music sequencers, or other forms of instrument controllers will allow you to use a synth as well. You can find synths without controllers of their own, and these are called sound modules.
One thing to note about synths is that they don’t have a way of producing actual sounds that can be heard. Instead, they just create the signals that other devices can use to create the sound.