All major ancient civilizations followed the motions of celestial bodies. They began to record these motions and measure the time it took for the sun to return each day. They did this for the moon as well, and for other heavenly objects they identified using at first rudimentary, then later more scholarly, means. The Sumerians and Babylonians originally devised calendars composed of 360 days --12 months of 30 days each. Days were divided into 30 parts (4 minutes each) of twelve 2-hour periods. Later, days were divided into 24 hours, and hours, minutes and seconds into 60.
The 360-degree year also established the original integration of circles using 360 degrees. Had the ancients chosen a calendar system based on 10, perhaps modern compasses would be made in 100 degrees. The sun comes full circle through the course of a year composed of 365 days, moving through 15 degrees of longitude per hour. But because 360 became the established number for all things circular, all globes, orbs and anything of circular shape subsequently became divided into 360 degrees.
On a compass, the 360 degrees can be broken down into 32 points taking up the four quarters. To list or recite all 32 points is called "boxing the compass." N, E, S, W, or north, east, south and west, are the cardinal points. They are at 0 degrees (N), 90 degrees (E), 180 degrees (S) and 270 degrees (W). The cross points -- NE, NW, SE and SW -- are between each of these. The remainder of the compass points fall in between the cardinal and cross points and are called "ordinal" points. Each of the 32 points is composed of 11.25 degrees.
When standing on the ground at any point on earth, all around you is a circle. Unless you are traveling and depend upon knowing where magnetic north is, you can relate to the concept of a compass by simply imagining the circle of space taking up your vision in every direction. Straight ahead of you could be assigned 0 degrees, to your right would be due east, behind you would be south and to your left would be west. Once you learn the movements of the sun or stars for orientation, you can actually place yourself facing north. Similarly, look at a clock face: north is noon, east is 3, south is 6, and west is 9. Each of these times has 90 degrees between them. All this is based on the origins of a circle as 360 degrees, but for safe travel in the wilderness, an actual magnetic compass would be advisable.