On the spring and fall equinoxes (around March and September 21), there is no tile of the earth with respect to the sun so the terminator line is parallel with the axis of the earth and with the lines of longitude.
The terminator line is at its greatest angle with respect to the axis on the winter and summer solstices (around December and June 21), when it is approximately 23.5 degrees off the axis.
The best way to understand the terminator line is to view it as it progresses through the day or through the seasons on a map or on an image of a globe. The Earth Viewer website provides this opportunity. Be sure to animate the image both in both daily and seasonal formats.