Resistance is actually quite a complicated thing to explain properly but the basic explanation that it is the effect of the material getting in the electrons way will suffice here. This theory describes electrons as having mean free paths through the metal, average distances they will travel before colliding with an an element of the lattice and being scattered forced to change momentum. Now ballistic electrons are those that exist in a material which have such low electrical resistivity that the mean free path of the electron is longer than the material that its travelling in. This means the electrons will only scatter and change direction when they meet the edge of the wire for instance, unable to escape due to the work function they ricochet back into the metal and continue on their elongated path until reaching another boundary.
Of course for this effect to be observed you don’t need to up the mean free path of electrons by cooling or removing purities or any of that hard stuff when instead you can just make a wire thin enough that the regular mean free path extends past it. Without scattering it is also possible to to imagine the electrons as waves propagating like electromagnetic waves in free space. With this in mind, two dimensional materials (which are of course thin enough for ballistic electron movement), have been designed to act like electron mirrors, beam splitters, lenses and wave guides.
However the inability to create a collimated beam of electrons in graphene has put a damper on these ideas as each require a much more ordered ray of electron then can currently be provided. However recent reports seem to show a promising design for a simple pinhole collimator that as the name suggests (get ready for an incredibly basic explanation) lets the electrons through a small hole which means that most that make it through are travelling relatively and then only the most parallel make it through the next small hole. The real breakthrough comes from the treatment applied to the edge of the holes makes them absorb electrons much more efficiently leading to stray electrons that did not properly traverse both holes being eliminated from the final beam. The result is a beam with only has angular width of 18° at a maximum, a marked improvement on previous attempts.