Abstract: The concept of fractal dimension is a development or extension of the concept of dimension in Euclidean geometry, while the concept of dimension itself comes from measurement in life and production. Dimension is a very common concept. When people want to measure the length, area or volume of a thing, it inevitably involves dimension. However, after the abstraction of mathematicians, dimensionality seems to have become somewhat unpredictable. Taking daily life, history, legend and other issues as examples, this article gradually uncovers the abstract veil on the surface of dimensionality and reduces it to a popular concept. The idea of fractal dimension can be understood by Euclidean geometry contrast. Either fractal geometry or Euclidean geometry, a power exponential relationship can be established by measuring scale (such as length), measure (length, area, volume, etc.). Its power reflects the dimension of the measured object. However, fractal geometry and Euclidean geometry have a dual relationship in measurement. Firstly, the measurement targets are different. The dimension of Euclidean geometry is uncertain, and the corresponding measure is needed; the measure of fractal geometry is uncertain in theory, and the corresponding dimension is needed. Secondly, the forms of expression are different. Euclidean geometry should be described by a positive power law, which gives the relationship between scale and measurement, while fractal geometry should be described by a negative power law, which gives the relationship between scale and measurement times. Thirdly, the emphasis of measurement is different. Euclidean geometry is based on measurement results and fractal geometry is based on scaling and measurement process.