Intensity in astronomy (commonly called radiance outside astronomy) is a measure of electromagnetic radiation striking a surface from a given solid angle, i.e., source. Alternately, electromagnetic radiation from a surface radiating within a solid angle can use the same measure. A common unit is watt per steradian per square meter.
d²Φ L = ———————— dAdΩcosθ Φ ≈ ——————— AΩcosθ
This is the common way the term intensity is used in astronomy. In physics, the term is often used all electromagnetic radiation striking a surface in watts per square meter. Thus the term "radiance" to distinguish meanings.
Specific intensity or spectral radiance is the intensity at a specific wavelength.
The mean intensity is the average intensity in all directions from a surface (perhaps within a solid angle), i.e., integrating it over the angle and dividing by 4π. It can be "specific", i.e., per wavelength. Using the mean is a useful way to simplify models.