Q:

Internal`WithTimeStamps usage

I was digging inside the Iconize implementation a little bit and saw that there's a function BoxForm`BoxFormAutoLoad which loads the FormatValues for objects.
For the most part it's boring, but one interesting function that I saw in it was Internal`WithTimeStamps. A sample usage of BoxForm`BoxFormAutoLoad is:
BoxForm`BoxFormAutoLoad[MakeBoxes, 
 IconizedObject["asd"], 
 StandardForm, 
 "NotebookTools`Iconize`", 
 {{IconizedObject, _}},
 Hold[IconizedObject]
 ]

And tracking the WithTimeStamps call inside we see it's running:
Internal`WithTimestampsPreserved[
 {IconizedObject},
 Apply[
  (BoxForm`wasProtected = Unprotect[#1];
    (* Uninteresting Which block removed *);
    Protect[Evaluate[BoxForm`wasProtected]]) &,
  {{IconizedObject, _}},
  {1}
  ];
 DumpGet[System`Private`$SystemFileDir <> 
   System`Dump`fixfile["NotebookTools`Iconize`"] <> "x"];
 ]

Running this seems to do nothing interesting so I'm wondering why it exists and in what way there are "Timestamps" in the call.

A:

It is an internal and undocumented function that can be used to prevent reevaluation of expressions whenever particular symbols contained in them change. This is a simple example:
Clear[a, b];
b = 1 + a

(* 1 + a *)

Internal`WithTimestampsPreserved[{a}, a = 1];
{a, b}

(* {1, 1 + a} *)

Although the value of a changed, the evaluator did not think that b might need reevaluation. 
That is because we preserved the timestamp of a, i.e. forced it to remain the same.
Contrast with the normal behavior where updating a also changed its timestamp, so now b is out of date and must be reevaluated.
a = 1; {a, b}

(* {1, 2} *)

In some sense, it accomplishes the opposite of Update, which can be used to force reevaluation in certain situations.

