The Great Sphinx of Giza was brought back to life when Mr. Crocker and Timmy were battling across time and space and arrived in Ancient Egypt. Mr. Crocker reanimated the Sphinx because Timmy's magical items were preventing him from attacking Timmy directly.
The Sphinx looks like a cartoon version of the real life version. Its eyes turn green when it is reanimated. After Crocker shoots off its nose, it returns to its original state, a reference to the actual Sphinx losing its nose.
During "Abra-Catastrophe!", Timmy Turner and his nemesis teacher, Denzel Crocker, were having a battle across time and space for control of his fairygodparents, whom had been captured by Crocker with the help of a Fairy-versary Muffin. They arrived in Ancient Egypt, with the pyramids still being constructed in the background. Mr. Crocker realized he could not attack Timmy directly because of the magical items he was carrying, so he reanimated the Great Sphinx of Giza which was behind Timmy. The Great Sphinx began to chase Timmy across the desert, until he used the Tooth Fairy's floss to create reins around his teeth. Timmy then directed the Sphinx to attack Crocker, who was pinned down for a moment until he shot off the Sphinx's nose, causing it to collapse back to its normal state.
The Sphinx then later appear erroneously as one of Timmy's Unwishes at Unwish Island in "Escape From Unwish Island", even though the Sphinx was not actually wished for or wished away by Timmy (as noted during a conversation between Timmy and Cosmo). It might have been put there because it was Cosmo and Wanda's magic which brought it to life, as other historical figures are present there as well despite their absence to reality having disastrous consequences on the time line, meaning they could simply be copies. The creators of the show also admitted this was an error.