In the pyplot document for scatter plot:
matplotlib.pyplot.scatter(x, y, s=20, c=\'b\', marker=\'o\', cmap=None, norm=None,
vmin=No
It is the area of the marker. I mean if you have s1 = 1000 and then s2 = 4000, the relation between the radius of each circle is: r_s2 = 2 * r_s1. See the following plot:
plt.scatter(2, 1, s=4000, c='r')
plt.scatter(2, 1, s=1000 ,c='b')
plt.scatter(2, 1, s=10, c='g')

I had the same doubt when I saw the post, so I did this example then I used a ruler on the screen to measure the radii.