What is the benefit of myelination of an axon?

Myelination of an axon makes propagation of action potentials along it much faster. In unmyelinated axons, the action potential is constantly regenerated by active propagation, with the depolarisation causing new action potentials to be constantly generated as it spreads along the axon. Myelination insulates the membrane from ion fluxes, meaning that propagation between nodes of Ranvier is by passive spread of currents in a local currents pattern, and regeneration of the action potential is restricted to nodes. This is much faster and is known as saltatory conduction. Though passive currents decay exponentially with time and distance, the distance and time between nodes of Ranvier are short enough that a signal can usually miss out 2 nodes and still surpass threshold to generate an action potential at the third. This is a safety mechanism.
The myelin sheath also acts as an electrical insulator of the axon by increasing the transmembrane resistance, reducing leak of signal across the membrane. This reduces the length constant of the axon, meaning that the passive currents between nodes decay less with distance, which helps the safety mechanism mentioned above. Modelling the membrane as a capacitor, myelination also reduces the capacitance by increasing the effective width of the dielectric. This quickens conduction because oppositely-charged ions on either side of the membrane are less affected by their electrostatic attraction to each other, allowing them to flow more freely.