The 2D discrete Fourier transform represents the image as a weighted sum of horizontal and vertical sinusoids. Low frequencies correspond to smooth intensity variation; high frequencies to fine detail and edges. The spectrum is centred: after fftshift the origin (DC) is in the middle.
Working in the frequency domain and transforming backA circular lowpass mask keeps frequencies below a cutoff radius and zeroes the rest. Because the image contains mostly smooth gradients and a few sharp edges, lowpass filtering retains the bulk of the energy and only faintly softens the circle boundaries.
lowpass: H(u,v) = 1 if sqrt(u^2+v^2) <= D0 else 0
highpass: H(u,v) = 0 if sqrt(u^2+v^2) <= D0 else 1
Interpret the spectrum
Most of the energy sits in the bright centre blob (low frequencies). A strong highpass mask keeps only thin bright edges around it. Raise the cutoff to see ringing in the spatial result.