Think in terms of magnitude (which can be positive or negative) and direction.

Think of a scalar. It has a magnitude but it doesn't have a direction. It's 0-dimensional.

Think of a vector. It has a magnitude (the size of the vector) and it also has a direction, which points in a straight line through the origin. It's 1-dimensional. For example, the vector (2,0,0) has magnitude 2 and points along the X-axis. You could write that as 2 * x, if x is the vector (1,0,0).

A bivector also has a magnitude, but instead of being 0-dimensional (like a scalar) or 1-dimensional (like a vector, it's 2-dimensional. So you could have a bivector that "points" along the entire XY-plane (remember: two-dimensional) and has some magnitude, say, 5. You could write that as 5 * x * y, if x is (1,0,0) and y is (0,1,0).

If you attach physical units to these things, then you might have units of meters for vectors, and square meters for bivectors.

Having an understanding of subspaces in linear algebra is helpful.

In a geometric setting - if you have two vectors, you can position them so that both have one end at the origin. This spans a plane (test it out yourself in 2D or 3D space with two pencils, put the eraser at the origin for each; it's a parallelogram). The area of the plane will depend on the length of the pencils. You can assign an orientation to the plane by imagining a rotor embedded in the plane that spins either clockwise or counterclockwise.

Do you know what a vector is? Vector:Line == Bivector:Plane

A vector is an oriented (+,-) magnitude(length) _in_ a line. A Bivector is an oriented (+,-) magnitude(area) _in_ a plane.

That area does not have any particular shape.