A dimension is something that qualifies a quantity (measure).
For an example, consider this: If I just say… “20kg”, it does not mean anything. But if I say, "20kg of Rice (Product) is sold to Ramesh (customer) on 5th April (date)", then that gives a meaningful sense. These product, customer and dates are some dimension that qualified the measure - 20kg.
Dimensions are mutually independent. Technically speaking, a dimension is a data element that categorizes each item in a data set into non-overlapping regions.