Although principally used to express the size of the area of a flat or 2D surface (a plane), it can also be used to represent the size of the surface of a 3D object (surface area, if you will).
In the International System of Units (SI), the standard unit of area is the square meter (signified as m²). This is an area the size of a square with edges 1m long.
To calculate the area of simple shapes such as triangles, squares, rectangles and circles there are a number of formulae computed by the ancient Greeks but when starting to compute the surface area of a more complex shape, you normally require the use of multivariable calculus which often requires a computer’s power to work out.
Area is also used a lot when describing the size of land or property for sale as it often correlates directly with the value. The use of terms like GIA (gross internal area) and NIA (net internal area) are still often expressed in terms of m² and ft² – meaning the square meters to square feet and square feet to square meters converters are popular tools.
External (and larger) areas are expressed in acres and hectares largely down to their relatively large unit sizes.