Metaballs are a family of implicit equations that are visually interesting and easy to set up. They all come in the form of a summation of some function of distance from a control point over a set of control points. The appearance of spheres/circles intersecting is a consequence of the popular falloff-type functions.

You can think of metaballs as a bunch of glowy points. The implicit surface that is shown is all of the points where the glows add up to some target value.