According to the definition of the book "Measure Theory and fine properties of functions." -Evans Gariapery a measure u is said of Radon if they are worth the properties described in the attached image.
According to the Wiki the motivation for this definition is to find a way to measure sets of a topological space so that this way of measuring is compatible with the topology of space.
In simple terms, what precisely would "find a measure that is compatible with the topology?" Answering this question gives the intuition behind Radon's definition of measurement?
