Think of A as a vector pointing someplace in a 5 dimensional space. Got that? It points somewhere.
Now, in 5 dimensions, we could imagine 5 axis vectors, all pointing in orthogonal directions to each other. We could now align ONE of those axes with the vector we just saw described in A. That leaves 4 other axis vectors all orthogonal to the vector A.
Now, typically, in 5 dimensions, we could imagine 5 axes, each one defined by the vectors comprising columns of the matrix eye(5).
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
So each row (or coliumn, for that matter) can be viewed as a vector pointing along one axis of a 5 dimensional cartesian space. Together, they span a 5 dimensional space, so any vector in that space can be represented as some linear combinations of the columns of eye(5).
But if we then rotated our R^5 space, so that one of those vectors were pointing in the same direction as the vector A, then the other axis vectors must also change, so that all were orthogonal to A.
A = [1 2 3 4 5]
1 2 3 4 5
B = null(A)
-0.26968 -0.40452 -0.53936 -0.6742
0.93591 -0.096129 -0.12817 -0.16021
-0.096129 0.85581 -0.19226 -0.24032
-0.12817 -0.19226 0.74366 -0.32043
-0.16021 -0.24032 -0.32043 0.59946
The columns of B are all orthogonal to the vector A. They can be viewed as together with A, an orthogonal set of vectors that still span the space. Clearly, you can see that A kills off any of the columns of B. (Ignoring the floating point trash that results.)
-2.2204e-16 2.2204e-16 -4.4409e-16 8.8818e-16
Essentially, whatever set of vectors you have in the rows of A, null finds a set of vectors that are orthogonal to the rows of A.
A realy good explanation of all this would also include an explanation of what orth does, as sort of the complement to null. But the best explanation would involve a course in linear algebra, and a good understanding of tools like SVD or possibly QR, to understand how those tools can be used to derive what null and orth produce.
I really wanted to add a wiki reference in this. It was hard not to do so. Sigh.