The Piano
The piano is the central image that takes on many meanings throughout the film. Initially, the piano symbolizes Ada's voice and her means of self-expression. Unable to speak to others, Ada pours her thoughts and emotions into her piano, such as when she is about to leave her home for Australia, or when she reunites with her piano after it was left on the beach. Over the course of the film, the two appear to become part of one another, blurring the line between art and the artist. This is reinforced most especially when, after Ada removes a key from the piano to send it as a message to Baines, Alisdair's discovery of her infidelity results in him chopping of one of her fingers. As they endure their new surroudings together, both Ada and the piano share similar consequences as a result of their experiences.
Additionally, because the piano is used to symbolize Ada's communication to others, it also serves as a link between Ada and those around her. While Alisdair refuses to carry the piano from the beach up to his house and forces Ada to leave the piano, Baines—after hearing Ada play—takes it up to his house and allows her to play there. Alisdair's refusal to allow the piano into his house becomes a refusal to allow Ada to be her own self, as she is forced to leave the instrument—a part of herself—behind. On the other hand, Baines's willingness to reunite Ada and her piano leads to their growing connection and subsequent romance.
At the end of the film, the piano embodies the legacy of Ada's experiences in Australia. When Ada, Flora, and Baines are being rowed to the ship that will take them away from Australia, Ada has the piano thrown off the boat, and is dragged into the water after it. However, her will to live leads her to cast off the ropes and let herself be pulled to safety. She is no longer bound to her life in Australia—which the piano has become tainted with—and is able to cast off a part of herself that before she considered integral to her identity. As a result, the piano coming to rest in the deep ocean symbolizes Ada's ability to move on from Australia, and the new beginnings that await her with Flora and Baines.
The Axe
The axe not only shows Alisdair's violent side, but also is an allusion to the story Bluebeard. Originally written by the Brothers Grimm, Bluebeard is the story of a man who marries a young woman every so often, only to murder her and go looking for a new wife once more. Earlier in the film, there is a scene where the organizers of the play show how shadows on a curtain might be used to present to the audience an axe killing a woman, when in reality the axe does not touch the actress at all. However, when Alisdair discovers Ada's infidelity, he seizes the axe he uses in his daily work and chops off her finger. Through the axe, Alisdair becomes a kind of "Bluebeard" by cutting off her means of playing the piano, which serves as an external embodiment of her identity and lifeline. The axe comes to symbolize the marital discord between Ada and Alisdair and the ultimate severance of their union when, at the end of the film, Alisdair allows her to return home.
Footprints & Paths
Ada gets Baines to come with her and Flora to the beach to get her piano. When Ada walks on the wet sand, she makes footprints that Flora follows in, which Baines then follows. This symbol of Flora and Baines walking in Ada's footsteps represents how both have a deep connection to her, and are willing to follow her wherever she goes.
However, these paths are dangerous to walk. Whenever Ada and Flora go to visit Baines, they must walk on narrow wooden walkways to avoid sinking into the mud. These symbolize how the connection between these three is not easy to maintain, and one misstep can result in undesirable consequences—for instance, when Alisdair chops off Ada's finger. Despite this, the earlier image of Flora and Baines following Ada's footprints in the sand emphasize the idea that their connections will endure, and ultimately culminates in all three leaving Australia as a family.
Barriers
Barriers is a recurring motif between people within The Piano. For instance, one night, Alisdair enters Flora's room while Ada is telling her about her father. He asks to give her a goodnight kiss, which she does not want to give him. This reinforces the fact that he is not her father, and as a result will not let him get as close to her as he hopes.
Another instance of barriers is when Baines wants to lie in bed with Ada during a lesson. She tells him it will cost him 5 black keys, as part of their negotiation for her to get her piano back. When she lies down, however, she is face down, indicating that she is closed off to him and won't let him get any closer to her.
Hole in Stockings
Baines asks Ada to raise up her skirt so that he can see her legs. Her stockings are revealed to have a hole, and Baines touches the skin that is shown through it. This symbolizes that, no matter how closed off she is to him, he is willing to find any way towards her, no matter how small. The fact that Ada does not prevent him from touching her bared skin adds to this, indicating that little by little, she will open up to him.
Pictures vs. Reality
When Ada reaches Australia, she is dressed before a mirror for her wedding photograph. She is told that she and her husband may not have a ceremony, but they will have the picture. The mirrored reflection of Ada and subsequent photograph both symbolize how this marriage is only an image, and not a connection based on anything that she truly feels in her heart.