These are initially statues of either NPCs, or Sims who are generated specifically for the statue.
In the future, there are a set of statues dedicated to Sims who did something special to set the future in it's current state, such as setting fashion trends or donating a lot of lottery winnings into funding for the future.The world of the future will change to reflect it's state, the utopia having giant flowers that release the same dew the happiness aerosol was made from, everyone being happy, and a permanent rainbow, while the dystopia has meteors landing constantly, trash all over the place, and people have took to eating bugs. The most impactful one is changing the course of the future into either a Utopia or a Dystopia, which requires doing a series of quests from Emit Relevart to either convince the military to spray an aerosol of happiness across the town to direct society to a utopian outcome, or to work with doomsayers to turn everyone apathetic towards the environment to create the dystopian outcome.The Sims 3 includes a couple of these for the Into The Future expansion.At several points in the level, manipulating the level in the past propagates into the present (such as when cremating an infested dog corpse in the past clears out a bloodfly colony in the present), but the biggest whammy comes at the end of the level, where knocking out or killing Aramis Stilton not only swaps out the entire level in the present, but also the level after that, as well as changing a number of other details, such as giving Megan Foster back her arm and eye. The Dishonored 2 level "A Crack in the Slab" sees the player character stripped of their mystical powers, which are replaced by just one - the ability to travel back and forth in time between the present and the night when the Big Bad Delilah was brought back from the Void.
For instance urging George Washington to chop down the fake cherry tree erases it from the future and sets Laverne free since she was hanging on the aforementioned tree.