Say you have an image which simply repesents a dot exactly in the center of the image ( black background, white dot). You at first fourier-transform this image row by row (horizontally). All the rows, but the centerrow, will be black ( the coefficients to all harmonics will be zero ). But the centerrow will contain a pulse, which will cause that the absolute value of all the (complex) coefficients to the harmonics in this row will be same. As such you know it's a pulse (dot), but you don't know its location.
Now you fourier-transform this first "horizontal" fourier-transform vertically (column by column), and all these vertical fourier-transforms will "see the horizontal line" having the same absolute coefficients. Again, by this vertikal transform, a pulse is seen in every column, which will cause that the absolute value of all the (complex) coefficients to the harmonics in all columns will be same. As such you know it's a pulse (line), but you don't know where it is located.
If you move this original dot in the image, the absolute values ( amplitude/power ) of all the coefficients in the whole image will be the same, but the phases of the complex coefficients to the harmonics will change, so you know the image represents a dot, and by inspection of the phases of these complex coefficients, you know where this dot is located in the image, and you can reconstruct the original image by inverse fourier-transform.
Rough: As for a dot, the absolute amplitudes tells you what it is ( how it looks ), the phases tells you where it is located. As for more complicated images, you can look at them as a sum of dots.