The term ballistic tranport refers to the transport of electrons in a medium where the electrical resistivity due to the scattering, by the atoms, molecules or impurities in the medium itself, is negligible or absent.
In general the resistivity is due to the fact that an electron, while moving inside a medium, is scattered by impurities, defects, or by the atoms/molecules composing the medium that simply oscillate around their equilibrium position (in a solid), or generically by any freely moving atom/molecule composing the medium, in a gas or liquid.
For a given medium one can associate to a moving electron a mean free path as the average length that the electron can travel freely, i.e. before hitting against something and deviating from its original path, possibily losing some kinetic energy. The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature (except for some material like semi-conductors).
Ballistic transport is observed when the mean free path of the electron is (much) bigger than the size of the box that contains/delimits the medium through which the electron travels, such that the electron alters its motion only by hitting against the walls.
In the case of a wire supended in air/vacuum the surface of the wire plays the role of the boxreflecting the elctrons and preventing them from exiting toward the empty space/open air. This is due to fact that there is an energy energy to be paid to extract the electron from the medium (extraction potential ).
E.g. ballistic transport can be observed in a metal nanowire: this is simply due to the fact that the wire is of the size of a nanometer (10 - 9 meters) and the mean free path can be bigger than that in a metal [1]