TraditionalForm[expr] prints as an approximation to the traditional mathematical notation for expr.
Output from TraditionalForm cannot necessarily be given as unique and unambiguous input to Mathematica.
TraditionalForm inserts invisible TagBox and InterpretationBox constructs into the box form of output it generates, to allow unique interpretation.
TraditionalForm can be edited in the notebook front end.
TraditionalForm uses special characters as well as ordinary keyboard characters.
TraditionalForm incorporates a large collection of rules for approximating traditional mathematical notation.
TraditionalForm prints functions in Global` context in the form f(x).
ToExpression[boxes, TraditionalForm] will attempt to convert from TraditionalForm.
The notebook front end contains menu items for conversion to and from TraditionalForm.
See The Mathematica Book: Section 1.10.9 and Section 2.8.1.
See also: StandardForm, TeXForm, MakeExpression, ToBoxes, MathMLForm.