Benoit Mandelbrot coined the term fractal from a Latin root.
Mandelbrot was trying to develop a "theory of roughness" to describe the geometry of the real world. He created fractal geometry.
Mandelbrot looked at measuring coastlines on a map (famously Great Britain). With a shorter and shorter "ruler" (and a higher and higher resolution map) you get a longer and longer measurement of the coastline because the "rulers" can fit into even more nooks and crannies of the rough/rugged coastline.
So the question about how long the coastline is depends on the length of the ruler you use to measure it since it' has self-similar roughness/ruggedness at different scales and is not smooth.