Covariance matrix explanation
You can't really have a covariance of a matrix.  What you can have, is a covariance matrix of a set of vectors.  So, if you think of the rows of your matrix A as two vectors in 3D: [2 3 4] and [5 5 6], then the covariance matrix of this set of two vectors is C = A' * A (A transpose times A).  Note that if you shuffle the rows of A in a different order, C does not change.

Now that you have C, you understood it correctly.  You can also do interesting things with the eigenvalues and eigenvectors of C.

Oops... Totally forgot.  Before you do anything, you have to compute the mean vector (column-wise mean of A) and subtract it from every row.