A solid angle (or angular area) is a size measurement for a region of possible directions from a point. For example, a region of a celestial sphere has a size, and the concept of solid angle quantifies that size.
One unit of a solid angle is the steradian (for square radian, which is adopted as a SI unit): the area on the surface of a SPHERE of the radius squared. 4π (roughly 12.6) steradians cover a whole sphere.
Another unit, the square degree is similarly defined for a degree: a degree has a length along a circle of π/180 and a square degree is that value squared. A square-like shape on the surface of a sphere, where each edge is a degree in length, following a great circle, is a degree long is actually slightly more than a square degree in size because of the curvature of the surface. Roughly 41253 square degrees cover a whole sphere and roughly 13283 square degrees cover a steradian.
Solid angles are used in the definition of some electromagnetic radiation measurements, and equations modeling spherical objects such as stars. They are also cited to describe the apparent size of astronomical objects (galaxies or nebulae), fields of view, and the areas covered by surveys. Square degrees are often used for the latter, but steradians are as well.