LNAV( lateral navigation ) & VNAV( vertical navigation)

RNAV is a short form of Area Navigation.

LNAV and VNAV are parts of the automatic flight director system(AFDS), and are short form for 'lateral navigation' and 'Vertical Navigation'. 

1.LNAV :is the route you fly over the ground or simply lateral movement of the aircraft w.r.t ground. The plane may be using VORs, GPS, DME, or any combination of the above.

As pilot enters his route as specified in 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.

2.VNAV means guidance to the pilot w.r.t to descent or climb or in simple words vertical movement of the aircraft.

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 short, 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 It is found the computer can almost always do it better and smoother.