As someone who has spent the last 7 years doing aircraft avionics systems testing I hope I can provide you with a satisfactory answer!
The ADC provides air data from pitot and static pressure sources, and also an air temperature sensor (usually total temperature). By means of look-up tables and a bit of maths the ADC then outputs various speeds and height/static pressure data. For navigation purposes the most important speed is True Air Speed (TAS), which is the speed the aircraft would be making over the ground if the airmass it was flying in was stationary. The aircraft TAS vector points in the direction of the aircraft heading (HDG), which on modern aircraft is provided by the INS / IRS / ADIRU depending on aircraft type.
Aircraft actual ground speed (GS) and track (TRK - which differs from HDG by the drift angle due to wind) are measured by GPS and/or INS / IRS depending on aircraft type, but if the aircraft is certified for area navigation (RNAV) it will almost definitely have a GPS. GPS cannot measure aircraft heading, so there will always be a sensor for this (e.g. INS or IRS), and neither can it measure TAS (or any other airspeed), hence the need for an ADC or ADIRU.
Once you have the HDG/TAS vector (from the ADC and whichever sensor provides heading data) and the TRK/GS vector (from the GPS or INS), a simple vector calculation will provide the instantaneous wind direction/speed vector. The 3 vectors always join up to form a triangle.
Hope this helps!
WF