From Bulbapedia, the community-driven Pokémon encyclopedia.
The Old Sea Map (Japanese: ふるびたかいず Old Sea Chart) is an event key item needed to access Faraway Island and subsequently catch Mew in Pokémon Emerald.
When the Old Sea Map is taken to the S.S. Tidal port in Lilycove City and the player interacts with the woman standing in front of the boat, the Faraway Island event will activate. Initially, the woman claims it's impossible to take the player to the area denoted on the chart, but Mr. Briney scolds her for turning the player away and volunteers to take the player to Faraway Island, even though it is a long way out of Hoenn.
After the boat ride, the player enters Faraway Island, a small island with a thick patch of forest. Deep within this forest, the player will notice Mew, who flees playfully. After a short game of hide and seek, the player is able to pin Mew in a corner and engage it in battle.
The Old Sea Map was only released officially in Japan and was distributed in 2005 during the Pokémon Festa event. Like the GS Ball, this event item never reached international players without the use of cheating.