The egg shell placed in the water will produce no noticeable observation. Water has a pH of 7, which places it in a neutral position on the pH scale. Water will tend to hold onto it's hydrogen ions and therefore offer no available potential to produce a chemical change.
Dilute hydrochloric acid, on the other hand, is a weak acid, somewhere in the vicinity of 4 to 6 on the pH scale. This means it will dissociate into hydrogen ions (H+) and chlorine ions (Cl-). The egg shell has a high concentration of calcium, which will combine in solution with the chlorine ions to form calcium chloride, a salt. The shell will noticeably dissolve, leaving behind the cell membrane, a rubbery, pliable substance that once served to house the interior of the egg.