VNAV stands for Vertical NAVigation. It is a mode available on more capable models of autopilot, specifically those capable of flying automatic instrument approaches.
When an aircraft is performing an instrument flight rules (IFR) approach, it is flying a three-dimensionally specified route. In addition to being required to follow a precise course (ground track) in order to properly reach alignment with the runway, the aircraft must also follow a specific glideslope. This glideslope - which may not be a consistent descent, but may have 'plateaus' in it, sections or level flight or of shallower descent - is surveyed and laid out to ensure that the aircraft not only reaches the runway threshold at the appropriate height and speed for landing, but to make sure that the aircraft avoids any obstacles or terrain that might be present.
A VNAV-capable autopilot can follow this three-dimensional pathway, generally down to minimums or the height at which the pilot must have the runway in clear sight in order to continue on to land. Some autopilots, those which can fly Cat III instrument approaches, are capable of flying all the way down to the runway - the fabled autoland, which has been around in some form or other since the late 1950s or early 1960s.
When the autopilot or flight management system is in VNAV mode, the aircraft's height will be constantly monitored and adjusted to conform to the glideslope for the published approach the aircraft is flying. In some cases, the FADEC is hooked into the autopilot or FMS, and the power settings can be adjusted by the computer as well. In others, such as the G1000 system used in general aviation, the throttle/propeller/mixture settings are controlled by the pilot - so the pilot must take care to adjust these as necessary during the descent to avoid overspeed or stall.
VNAV mode is in contrast to other modes such as Altitude Hold (self-explanatory) or VS (Vertical Speed) which simply maintains a constant level of climb or descent. To fly a precision approach, the autopilot must also be able to operate in LNAV - Lateral Navigation - to navigate the approach.