Quaternion understanding

I want to understand the quaternion. Mostly I didn’t used quaternion for rotation I used Quaternion.Euler(Vector3), because that’s the values from inspector. I want to understand why quaternion has 4 components(x, y, z, w). What they represents. Please don’t send me the unity documentation page because I saw it and it isn’t explicit. I found something on answers.unity.com but I didn’t understand very well. It is something about trigonometry sin, cos of angles on the circle of rotation.

The Unity manual doesn’t cover it well because it isn’t something you probably need to learn. You can just treat it like a black box. But if you insist, Wikipedia has a more expansive explanation, though it looks like it may be confusing without a strong mathematics background.