By law (FAA regulations), all intentional parachute jumps must be made with a single harness, dual parachute system with both a main canopy *AND* a reserve canopy. In other words, you have a second (or spare) canopy in case the first one fails to open properly.
However, it must be noted that the technology utilized in today’s sport parachuting equipment is light years ahead of the old military surplus gear used in the ’60s and ’70s. The canopies are DRASTICALLY different from the classic G.I. Joe round parachutes. The materials are stronger, lighter and last longer, the packing procedures are simpler, the deployment sequence is much more refined, etc.
The reserve canopies are even more carefully designed and packed. The reserve parachute must be inspected and repacked every 180 days by an FAA rated parachute Rigger – even if it has not been used during that time.
The student’s main canopy is always packed either by a rigger or under a rigger’s direct supervision by experienced packers.
There are also additional safety features employed to ensure canopy deployment such as Automatic Activation Devices (AAD), Reserve Static Lines (RSL) and Sky Hooks which add still more layers of safety.