Make a formatting structure whose interpretation is not based on its appearance:
Out[1]//DisplayForm= |
| |  |
An InterpretationBox is interpreted as the expression in its second argument:
| Out[2]= |  |
Copying the interpretation box and using it as input also evaluates the hidden interpretation:
| Out[3]= |  |
InterpretationBox is used in the standard formatting of Interpretation objects:
Out[1]//FullForm= |
| |  |
The first argument of the InterpretationBox gives its visible format:
| Out[2]= |  |
The TraditionalForm formatting for many built-in functions uses InterpretationBox:
| Out[1]= |  |
In the typeset result, the letter 
stands for EllipticNomeQ:
Out[2]//TraditionalForm= |
| |  |
The InterpretationBox allows this form to be used as input without losing its meaning:
| Out[3]= |  |
