As far as SFML is concerned, the origin gives the origin of the texture in the sprite.
For example, let's assume we have a square :
doing
square.setOrigin(width/2, height/2);
will mean that our texture won't be displayed from position, but from position-origin, meaning that our square image will have it's center at the "position" indicated, and no longer its left-top corner.
The origin is also the rotation center.