TraceDepth is an option for Trace and related functions which specifies the maximum nesting of evaluation chains that are to be included.
Setting TraceDepth -> n keeps only parts down to level n in nested lists generated by Trace.
By setting TraceDepth, you can make Trace and related functions skip over "inner" parts of a computation, making their operation more efficient.
See The Mathematica Book: Section 2.5.10.
See also: TraceOff.