Step 1: Understanding Leydig Cells.
Leydig cells, located in the interstitial spaces of the testes, are responsible for producing testosterone, the primary male sex hormone. Testosterone plays a key role in male sexual development, including the development of secondary sexual characteristics such as deepening of the voice and facial hair, as well as promoting spermatogenesis.
Step 2: Conclusion.
Thus, the function of Leydig cells is to produce testosterone.
Final Answer:
\[
\boxed{\text{Leydig cells produce testosterone.}}
\]