Area is the mathematical measure of the amount of 2-dimensional "space" on some 2-dimensional surface. That surface is often an ordinary flat plane, but doesn't have to be—it might be the surface of a sphere, for example. The portion of the surface whose area is to be calculated might be that enclosed by a set of lines, or some other way of limiting it. Area is often calibrated in terms of some abstract "unit squares". For example, on a plane, the area might be calibrated in "square units". In a practical application, that might be square inches or whatever.
The area of a rectangle can be found out by multiplying the length of the space by its width. The units are presented as a unit of length (inches, feet, meters, centimeters, etc.) squared.