After you leave the Great Plateau, something strange will happen at night. The sky glows red, the air around you will fill with glowing, red embers and ash will swirl all around. When the moon rises, it is red — it’s the Blood Moon.
What is a Blood Moon?
Think of a Blood Moon as Legend of Zelda: Breath of the Wild’s reset button. All of your enemies respawn, and the world’s resources — things like ores or the weapons you find laying around — repopulate.
… Link … Link … Be on your guard. Ganon's power grows … It rises to its peak under the hour of a blood moon. By its glow, the aimless spirits of monsters that were slain in the name of the light return to flesh. Link … please be careful.
What does a Blood Moon mean for me?
First and most obviously, a Blood Moon means all of your enemies are back.
Harder to notice, though, is a subtler mechanic tied to the Blood Moon. Over time, as you repeatedly kill the same enemies, they come back tougher. That low-level red bokoblin that you killed might come back as a stronger blue bokoblin. This series of evolutions generally runs red, blue, black, then silver, though this isn’t true for all enemies — there’s no silver hinox, for example. It’s not just that the enemies are tougher, though. They’re also better equipped — which is good news for you and your looting.
Your enemies will respawn inside shrines, as well. With a little (a lot of) work and a little (a lot of) patience, this will let you (basically) farm the Test of Strength guardians for better and better guardian weapons.
The other, even more subtle effect of a Blood Moon is that it will add a buff to anything you cook during that night. It’ll be a little extra of whatever the meal normally provides — a few extra hearts of healing from a meal or some extra effect time on an elixir.
Can I cause a Blood Moon to happen?
Short answer: No.
Blood Moons appear to be random, or at least follow their own inscrutable logic, kind of like shooting stars.
There’s a lot of anecdotal methods for triggering a Blood Moon event, but we couldn’t recreate the result (nor could most of the commenters in that thread). Other players suggest — again, anecdotally — that the number of enemies or overworld bosses you kill will make a Blood Moon more likely. This makes sense, seeing as a Blood Moon respawns all of your enemies. But without a look under the game engine’s hood or a better sense of what "more likely" means, it will still feel random.