I don't understand what this theorem for a characterization of the determinant actually means, and what use it has. Could you please explain it?

Let D be a function mapping from the set of square matrices M with n rows/columns over the field F, to a field F. Also let D be a function that is multilinear and alternating in columns. Then

D(A)=D(I)detA

Let D be a function mapping from the set of square matrices M with n rows/columns over the field F, to a field F. Also let D be a function that is multilinear and alternating in columns. Then

D(A)=D(I)detA