Electrolytic capacitors are
formed during manufacturing. Forming produces a reaction between the anode and the electrolyte (anodization) that grows a thin dielectric layer. The dielectric is what makes it a capacitor, and its thickness determines the capacitance, voltage rating, and leakage. Over years of storage without charge, the anodization can dissolve back into the electrolyte, which reduces the voltage rating and increases leakage.
Reforming is just repeating the procedure that grows the anodization. Since the capacitors are not new, and the electrolyte may have evaporated or degraded, the results are not always as good as new. This only happens with
electrolytic capacitors. Reforming film capacitors is a non sequitur.
Note: anodization is a current-controlled process, not a matter of "bringing up the voltage slowly". A variac is not the best way to reform capacitors, although it can prevent inrush surges from damaging vulnerable parts. But some regulator topologies become unstable and can be damaged this way.