You need to add another line to your code.
  On Error GoTo ErrorHandler

I would also add another variable to your routine
  Dim StrDescription as String
and try to assign the Description property to that variable for use in you
append query.

Also, I would add a test to eliminate system tables (they start with
"MSys"), but you may want them listed.  Obviously, this is your choice.

If Instr(1,Tdf.Name,"MSYS") <> 1 then
  ' Do the work
End If

Public Sub EnumerateTables()
  Dim db As DAO.Database
  Dim tdf As TableDef
  Dim fld As Field

  On Error GoTo ErrorHandler

   Set db = CurrentDb
   DoCmd.SetWarnings False
   For Each tdf In db.TableDefs
       'Get the description and add quote marks around it
       'and handle any description that has a quote mark in it
       'by doubling the internal quotes.
       strDescription = Chr(34) & _
              Replace(tdf.Properties, Chr(34), Chr(34) & Chr(34)) & _
              Chr(34)
       'if that errors then the errhandler kicks in and assigns the string
"NULL"

       DoCmd.RunSQL "INSERT INTO tblTableDefs" _
           & "(tableName, TableDesc) " _
           & "VALUES (" & tdf.Name & ", " & strDescription &  ")"
       Next tdf

       DoCmd.SetWarnings True

Exit Sub
ErrorHandler:
   Select Case Err.Number
       Case 3270
           strDescription = "Null"
           Resume Next
       Case Else
           MsgBox Err.Number & ": " & Err.Description
           Resume
   End Select

End Sub