How to understand the data set with 3D Surface xyz axis?

I usually think about it by imagining the 25 x 25 matrix as pin impression art where the height of the pin at row i, column j is determined by the value at row i, column j in the matrix. While it is possible to create a surface plot from a list of points in 3-space like you mentioned, it is easier to do it using a 2-D matrix.