TableDepth is an option for TableForm and MatrixForm which specifies the maximum number of levels to be printed in tabular or matrix format.
TableForm[list, TableDepth -> n] prints elements in list below level n as ordinary lists, rather than arranging them in tabular form.
With the default setting TableDepth -> Infinity, as many levels as possible are printed in tabular form. In TableForm, the levels printed need not consist of elements with the same list structure. In MatrixForm, they must.
See The Mathematica Book: Section 2.8.8.
See also: TensorRank.