If you are using color photos, you should first convert the selected area from RBG (red, green, blue) to HSL/HSV (article).
HSL stands for "hue, saturation, lightness".1 The number you are interested in is the lightness.
In the most general terms, the lightness refers to how you perceive the brightness of a colored surface. It's hard to use the red/green/blue components to say whether a patch of red is brighter/darker than, say, a patch of blue. Converting to HSL takes care of that problem.
Once you have done the conversion, you can simply average the lightness values of your selected area.
Quick note on lightness values: Technically, you can't simply average the lightness values because the perception of lightness is not linear (article). But, unless you are writing a deeply scientific application, simply averaging the lightness will give you an "accurate enough" value.
1 In Adobe Photoshop, they call it HSB (hue, saturation, brightness)