The size of the box plays a key role in many measurements. The average value and noise number displayed at the top of the Examine Image screen gives the average pixel value in the box and the noise is the RMS deviation from that average. When you set the background threshold with the T key, the average value at that point is stored for future use.
The magnitude measurement depends upon the background threshold, as this value is subtracted from the measurement of a star field to isolate the star's contribution. Likewise, the 'Point' or 'Position' (P key) function subtracts the background to isolate the star's contribution for calculating the center of the stellar image.