The contest between Athena and Poseidon is said to have left several traces on the spot of Erechtheion. It was Cecrops who asked them to offer a valuable gift to the city. According to the legend Poseidon struck his trident creating a stream of water, while Athena struck her spear in the ground planting an olive branch and creating the sacred olive tree as a symbol of peace and prosperity on earth. The olive tree was considered more valuable, hence Athena was given claim of the city and Athens was named after her.
"[…] It was Poseidon who came first to Attica, and stroked his trident and produced the sea they now call the Erechteius. Then came Athena and made Cecrops witness her claim of possession, and planted an olive tree which can still be seen in the Pandroseion. In the dispute over the land, Zeus appointed the twelve gods as judges. Their verdict was in favor of Athena, since Cecrops testified that she had planted the olive first. Athena therefore named the city Athens after herself, and Poseidon, furious, flooded the Thriasian plain and left Attica under water."
"[…] The olive tree, the salt spring, and the marks of Poseidon’s tridents were some of the most venerable and sacred spots on the rock (though Pausanias was not terribly impressed with the spring), and they were certainly regarded as marvelous signs of the primeval contest." [Hurwit: Acropolis in the Age of Pericles]