The circles do not look smooth because of quantisation the need to split the plane up into discrete cells. The cells are often called bins.
However, the two cells that get 2 votes each are the candidates for the centres of circles that pass through the two features.
This is repeated for each feature.
Note that this is different from convolution, where the basic operation is carried out for every element of the output array. Here, the main loop is over features in the input. This can be very fast. Parallel implementation is also possible.