Role in the film
Anamaria had sailed with Jack Sparrow prior to this, but the pirate captain had stolen her boat, the Jolly Mon - or, as Sparrow himself put it, "borrowed without permission, but with every intention of bringing it back", though he never did, as the Jolly Mon sank at the Port Royal harbor moments after Jack disembarked on the dock.
This deed was not forgotten by Anamaria, who made a point of reminding Jack of his transgression when they met again in Tortuga. In an attempt to placate her, and ensure she would join his crew, Jack promised to give her another vessel, which, due to Will Turner's intervention, he was forced to concede would be the Interceptor.
Indeed, Anamaria steered the ship after Turner rescued Elizabeth, since Jack had fallen behind during the rescue on Isla de Muerta. She was able to outrun the Black Pearl for a time, and engaged its cursed pirates in combat when Barbossa's ship caught up. The crew were ultimately captured and the Interceptor destroyed, and soon after Anamaria and the others found themselves locked in the brig of the Black Pearl.
When the ship returned to Isla de Muerta, Elizabeth infiltrated the Pearl and rescued Jack's crew, hoping they would help her rescue Will. However, the pirates, recalling Jack owed them a ship, decided to take the Black Pearl instead. Sometime later, during the planned hanging of Jack Sparrow, Anamaria steered the Black Pearl to Port Royal, where it awaited Jack's escape. With the help of Will Turner, Jack evaded the noose, and fell over the fort. The Pearl rounded the cove, and Jack was brought on board. Anamaria handed over command of the ship to Jack, content to serve simply as one of his crew.
Since Anamaria was not seen in the sequels, it can be assumed she and Jack parted ways and Jack got her another ship.