I wish to calculate the average NDVI value of an area (polygon). Thus the average value of all pixel.
How can this be done in QGIS?
QGIS has a plugin called zonal statistics that will allow you to calculate the mean NDVI. It will also calculate the pixel count, and the sum of all pixel values within each polygon.
If you wish to sample multiple rasters, I'd recommend using the Zonal Stats module in RSGISLib. This will allow you to iterate over multiple rasters using the same shapefile, exporting the data as a CSV or an ESRI shapefile.