It is a more compact way than an m-by-n rectangular array by exploiting a special structure of the matrix.
Typical examples of matrices that can take advantage of packed storage include: The packed storage matrix allows a matrix to be converted to an array, shrinking the matrix significantly.
[1] Consider the following upper matrix: which can be packed into the one array:
Similarly the lower matrix: can be packed into the following one dimensional array: Both of the following storage schemes are used extensively in BLAS and LAPACK.
An example of packed storage for Hermitian matrix: An example of packed storage for banded matrix: