Originally, the compass rose was used to indicate the directions of the winds (and it was then known as a wind rose), but the 32 points of the compass rose come from the directions of the eight major winds, the eight half-winds and the sixteen quarter-winds. Each point is indicated by degrees, with 0º for North, 90º for East, 180º for South and 270º for West.
The 32 points are therefore simple bisections of the directions of the four winds (but the Chinese divided the compass into 12 major directions based on the signs of the Zodiac). North is usually at the top, and each direction is abbreviated using its first letter (N for North, E for East, etc.)
The compass rose above is divided into subsections so NE is northeast, NNE is north-northeast, NbE is north by northeast, etc. One of the first things western apprentice seamen had to know were the names of the points.
Here are some simpler but very colorful versions of the compass rose:
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