In plain English:
Tie a string tightly around a globe.
It will lie in a perfect circle, known as a "great circle".
This can be done only if the string is stretched tightly around the full circumference; it will fall off if moved slightly in any direction.
The circle can be oriented in any way, but on a globe with markings, obvious positions are along the equator, or along any meridian, passing through both north and south poles.
A great circle passing through any two points represents the shortest distance between them when traveling along the surface.
This is why plane flights from Los Angeles to Hanoi, which is even farther south, pass near the Aleutian Islands in Alaska.
Imagine you are navigating a ship or plane using only a compass.
The simplest and least error-prone method would be to maintain a constant heading throughout the entire trip.
From Portugal, if you continuously sail south-west, you will reach Brazil.
It won't be the shortest or fastest route, but it will be the easiest.
The Mercator Projection map (the "evil one", that makes Greenland look larger than Africa) was designed specifically for this purpose.
Draw a straight line from your start to your destination and that course will have a constant heading all the way.
Without any adjustments along the route, your compass will always indicate the same direction to go.
Every straight line on a Mercator Projection map is a rhumb line.
Except when following the equator (which is both a rhumb line and a great circle), any rhumb line will eventually reach either the north or south pole.