What purpose do diodes that do not emit light serve in electric circuits?

Answer 1

Diodes are always placed in a circuit to control the direction of current flow

One major application is convert Ac to Dc.

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Answer 2

Diodes are devices that have a high resistance to current in one direction but a low resistance in the other direction. Thus, they are useful in cases when you want unidirectional current flow; that's why Wikipedia calls diodes an "electronic version of a check valve." (https://en.wikipedia.org/wiki/Diode). Light emitting diodes are diodes that also happen to emit light when they pass current.

Diodes are also the building blocks for semiconductor circuit elements, specifically transistors. It is the unidirectional flow of a diode that makes it an apt building block for a transistor because transistors act as switches in digital circuits.

In summary, diodes have a number of purposes, whether they emit light or not.