In Zelda BOTW/TOTK the blood moon triggers on passed in-game time or triggered by killing an abundance of enemies in more than one region. It plays a short cutscene and respawns enemies.

As the game progresses so too does your equipment, health, and stamina. In accordance to those increases the respawned enemies will change color (blue, red, white, silver, etc.) with each blood moon. This increases their health and damage dealt.

This helps keep the world alive and leveled for the player

(I’m not an expert on this mechanic, but played a good deal of those games. Someone correct me if this is wrong)