In Quantum Electrodynamics (QED), the most accurate description of electrons we have right now, lectrons are point particles and don't have any shape. However, sometimes something called "classical electron radius" (see, e.g. wikipedia) is specified which would be the size a classical charge distribution of the total charge of the electron would have to have if its mass were entirely due to the energy of the
electric field it produces. It is about the 10^(-15)m specified above. In QED, this is the distance below which the spontaneous production of electron-positron pairs becomes important, that is, where the single particle picture breaks down.