A great circle is any circle that is drawn around the Earth where the centre of the circle is the centre of the Earth. For example, the equator is a great circle.
The shortest distance between two points on the surface of the Earth is always along the great circle that passes between the two points. This is known as the great circle distance.
A small circle is any circle that is drawn around the Earth where the centre of the circle is not the centre of the Earth.
Another way to think of it is that all great circles will divide the Earth into 2 equal parts, but all small circles will not.
All parallels of latitude (except the equator) are small circles.
A rhumb line is a line that crosses all meridians of longitude at the same angle.
All parallels of latitude are rhumb lines.