The statue depicts the town founder Jebediah Springfield standing over a dead bear he 'killed with his bare hands', reflecting a popular folk tale involving Jebediah Springfield (however, recent studies suggested that the bear actually killed him instead).
Bart Simpson once stole the head of the statue, causing public outrage. He did this because he thought Dolph, Jimbo and Kearney would think it was cool. However, they later said that it was just cloud talk, and Bart later puts the head back on the statue.
The statue was unscathed by the events of Trappuccino, which sent the entire town into ruin. In the new opening sequence, Kearney and Jimbo cut off the head of Jebediah Springfield which falls on Ralph Wiggum.
The statue appears in the new HD Opening Sequence. Ironically, the opening sequence involves Dolph, Jimbo and Kearney sawing the statue's head off, which falls on top of Ralph Wiggum (who said something different each time, Season 20 only).
It also appears in various video games. Most notably, in The Simpsons: Bart vs. the Space Mutants, if Bart scares a bird off from the statue with a firecracker, Jebediah will congratulate Bart for the deed, and then give him advice about how victory comes to those who get "ahead." (which is presumably a reference to the shortcut in one of the buildings to the Springfield Retirement Castle).