One purpose of the glass beads is to disrupt the flow of vapour by convection to improve mixing and attainment of thermal equilibrium at each level of the fractionating column. This creates a steeper, smoother temperature gradient. Without the beads (or similar 'baffles') convection currents would bring vapour at different temperatures and compositions to the same level, making the temperature gradient much less distinct and the composition inhomogeneous. A much longer column would be needed, and fractions tapped off at a given level would be less pure.
The solid surface of glass enables heterogeneous condensation which has a smaller energy barrier than homogeneous condensation in the body of the vapour. A flat or concave surface reduces the contact angle, which in turn reduces the area and energy of a vapour droplet forming on the surface, and speeds up the rate of nucleation. This favours beads with large radius. Increasing the area of the surface at which nucleation takes places increases the rate at which vapour/condensate can change phase; this improves attainment of thermal equilibrium. This favours beads with small radius. Surface area could be increased by using microscopic particles floating in the vapour, but they would move around very easily and be difficult to control; the contact angle for nucleation would also be much greater; and there would be a much wider distribution of temperatures at the nucleation sites. Ideal bead size is a compromise between the needs to maximise surface area and minimise convex curvature.
Glass is used because it is chemically very stable. It reacts with very few substances (hydrofluoric acid being a rare exception). I presume that the low thermal conductivity of glass - compared eg with metal - aids in making the temperature gradient steeper, reducing the length of the column.