It commemorates the Battle of Hoover Dam. The rangers lured the best of Caesar's Legion into Boulder City, then blew the whole town up. The NCR still lost a bunch of troops in the fighting, though. My older brother sacrificed himself so they could evacuate some of the wounded.
His brother, Donald Kowalski, died at the battle of Hoover Dam. When the player meets him, he is on leave and plans to go home to see his family in California, but before he goes on his way he wanted to pay his respects at the memorial.
Private Kowalski does not remain at the memorial indefinitely, and will disappear from the game world some time after the Courier arrives near Boulder City.
Defacing the Humble Stone: Desecrating (shooting or otherwise harming) the Boulder City memorial will make a Speech prompt and, depending on the Courier's selection, may make him become hostile. Killing him will give NCR infamy. If the Courier passes the Speech check, and he/she shoot or harm the memorial again, he will not open fire. Calling him and his brother a "bitch" will cause him to become hostile.