Here's a synopsis:
RNAV is short for 'Area Navigation'. In the old days you used to have to fly directly over the navigation aids on the ground (VOR, NDB etc) to make your route. It meant a slightly zig-zag course for your flight as you couldn't get the navaids in a perfect line between every possible city pair. Then when computers started getting into planes, it was possible for the computer to 'create' an imaginary navigation aid based on a direction and distance from a real one on the ground. So you could draw a straight line from your origin to destination, and create the waypoints based on the computer figuring the direction and distance from some nearby navaids (usually VORs) and using that to fly a straight route. Nowadays, RNAV is also loosely used to describe any 'straight line' navigation method like GPS, as well as the old RNAV method too.
LNAV and VNAV are parts of the flight guidance system, and are acronyms for 'Lateral Navigation' and 'Vertical Navigation'. I don't know the 737 very well, but I'd bet the 767 I fly is very similar.
LNAV is the route you fly over the ground. The plane may be using VORs, GPS, DME
, or any combination of the above. It's all transparent to the pilot, as he enters his route as specified in the clearance and flight plan into the FMS (Flight Management System). The route shows up as a magenta line on the lower flight display, and as long as the autopilot is engaged in the LNAV mode, it will follow that line across the ground. LNAV however does not tell the plane what altitude to fly, and that is where...
VNAV comes in. Vertical Navigation is where the specified altitudes at particular waypoints are entered into the FMS, and the computer figures the best way to accomplish what you want. For instance, if you are flying with the autopilot on in VNAV mode at cruise altitude, you can enter what speed you desire to make a descent at, and what altitude you wish to cross a particular point, and the computer will figure out where to bring the throttles to idle and begin a descent, to allow you to cross to that point in the most economical manner. VNAV also works in climb. There are airspeed restrictions at various altitudes, and if you are in VNAV, it will fly the plane at the desired power setting and angle to achieve the speed (and efficiency) you wish.
In reality, we spend most of our flying with both LNAV and VNAV engaged. If the autopilot is off, LNAV and VNAV still send their signals to the flight director so we can hand fly the plane the way the autopilot would if it were flying.
So in summary, RNAV is a method of navigation, and LNAV/VNAV are subsystems of the autoflight system. LNAV is the course (in 2 dimensions) across the ground, and VNAV is the flight path (in 2 dimensions) up and down. Of course we can do it by other methods which worked well for many, many years. But I've found the computer can almost always do it better and smoother. A word of caution is always given to pilots when first learning the LNAV/VNAV system though; it's best to study well and always keep an eye on what it's doing. It is only as good as the person punching the buttons, and the most common thing heard in today's modern cockpits is "What's it doing now???"
One smooth landing is skill. Two in a row is luck. Three in a row and someone is lying.