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You might think out of the 360° in a circle being off by only 1° is not a big difference and for a very short distance, that may be true. Let’s look at what that means if we are hiking or more significantly flying.

Consider this. If you're going somewhere and you're off course by just one degree, after one foot, you'll miss your target by 0.2 inches. Trivial, right? But what about as you get farther out?

After 100 yards, (one football field) you'll be off by 5.2 feet. Not huge, but noticeable.
After a mile, you'll be off by 92.2 feet. One degree is starting to make a difference.
After flying from San Francisco to L.A., you'll be off by 6 miles.
If you were flying from San Francisco to Washington, D.C., you'd end up on the other side of Baltimore, 42.6 miles away.
Traveling around the globe from Washington, DC, you'd miss by 435 miles and end up in Boston.
In a rocket going to the moon, you'd be 4,169 miles off (nearly twice the diameter of the moon).
Going to the sun, you'd miss by over 1.6 million miles (nearly twice the diameter of the sun).
Traveling to the nearest star, you'd be off course by over 441 billion miles (120 times the distance from the earth to Pluto, or 4,745 times the distance from Earth to the sun).