what is stress?

Consider an elastic body of some kind - any solid material will do. Anything from a sponge to a brick can be compressed or stretched if enough force is applied to it. Some materials are very strong in compression, but weak in tension (stretching), like a brick or piece of concrete. A rubber band or a rope might be strong in tension, but would be hard to compress just because of it's shape.

Anyway, the light blue object on the left represents an arbitrary part (volume) of this elastic body, which has to be imagined as three-dimensional, since I've only drawn it in two. This part must be inside the body, and could include some of its surface (but doesn't have to).

My drawing is a little off, but the point x is supposed to be on the imaginary surface of this arbitrary volume within the body (not necessarily on the surface of the body).

Now consider a unit vector n ("unit" because it has the value of one in whatever unit of length you want to use - inches, centimeters, etc) which is perpendicular to this imaginary surface right at the point x. By the way, I'm using bold face letters for vectors.

Maybe I should stop here and explain about vectors. A vector has both a value, say 1 cm, and a direction, like north or south. In physics, we use a coordinate system to specify both position in the space, and direction. Since we are talking about three-dimensional objects, we choose one point in the space as the origin, as a reference point. Then all other points in the space can be identified by their distance from the origin, and in what direction you would go from the origin to find them.

So the point x on the surface in the drawing can be represented by three numbers - x,y,z - which are the distances along each of the three perpendicular axes in a rectilinear coordinate system. (Later on we'll want to label the axes x1, x2 and x3 instead of x,y and z).

I'll close for now and try to make a drawing of a coordinate system, that might clarify the explanation somewhat.