The origin, of something, is the location from which it originated; that is, from whence it came.
The origin (from the latin origo, "beginning") in a coordinate system is the point where axes of the system intersect. The most common systems are two-dimensional (contained in a plane) and three-dimensional (contained in a space), having therefore two or three perpendicular axes. Axes are then divided in two halves from the origin, a positive and a negative one. This is usually done by defining a point of interest to us, and calling "positive side" the halves of the axes being closer to this point. Axes are usually called "X" and "Y" (in a plane) or "X", "Y" and "Z" (in a three-dimensional system).
All positions in the plane or space are then located in reference to the origin in terms of "5 distance units in direction of the positive half of the X axis" and "10 distance units in direction of the negative half of the Y axis" for a two-dimensional system, adding the part for the "Z" axis (for instance "12 distance units in direction of the negative side") in case of a three dimensional system. All this can be written in short as (5,-10,-12), which is the position of the point in reference to the origin, also known as the coordinates of the point. The coordinates of the origin are always (0,0) or (0,0,0), depending on the type of system.