The coordinate system origin is the point on the Earth (specified as longitude and latitude degrees) from which all coordinate distances are to be measured. X = 0 and Y = 0 at the origin point, unless a false easting and/or false northing is used. It is chosen to optimize the accuracy of a particular coordinate system. As we move north from the origin, Y increases; X increases as we move east. These coordinate values are generally called northings and eastings.
For the Transverse Mercator projection the origin's longitude defines the central meridian. In constructing the Transverse Mercator projection a cylinder is positioned tangent to the earth. The central meridian is the line of tangency. The scale of the projected map is true along the central meridian.
In creating a Hotine Oblique Mercator projection it is necessary to specify a great circle that is not the equator nor a meridian. MapInfo Pro does this by specifying one point on the ellipsoid and an azimuth from that point. That point is the origin of the coordinate system.