You're not a pilot, you're a passenger, and an arrogant one at that. The "auto landing" they were referring to was probably the ILS -- it's a beacon that is positioned at the start of the runway and allows for instrument landings. Every landing is an "auto" landing on a passenger craft because they're flying instrument flight rules.
They do not just push a button in the cockpit and then nip off for a bit of tea while the plane magically lands.
girlintraining, let's give you a little more training, since you obviously need it.
The ILS ( Instrument Landing System ) provides vertical and lateral guidance to the touch down zone of the runway. 'Beacon' is usually used to refer to an NDB (Non-Directional Beacon).
The pilot may follow ILS guidance manually, or he may 'couple' the autopilot to the ILS and have the autopilot fly the approach. Typically they disconnect the autopilot at low altitude and land manually.
Most airliners built since the 80's have 'autoland' capability. That means that in addition to flying the approach, the autopilots have the ability to complete the flare, landing and rollout without intervention of the pilots. When the visibility goes below certain minimums autoland is the only way you can legally or practically land the aircraft. Pilots (and the aircraft itself) monitor autolands very closely for signs of failure.
They do not just push a button in the cockpit and then nip off for a bit of tea while the plane magically lands.
Correct, there are multiple buttons, for multiple redundant autopilots. And you're correct, no tea. We're already pretty wired at this point.
For the others confusing 'fly-by-wire' with autoland, fly-by-wire refers to pilots control inputs feeding a computer which in turn commands the flight controls to move. Airbus A320 and later and Boeing 777 and later use fly-by-wire.
In earlier aircraft, there is no computer intermediary between the pilots controls and the control surfaces. Essentially, it's just cables and hydraulics between the two.
Autolands are routinely accomplished by both fly-by-wire and conventionally controlled airliners.