The piano, a Kawai studio upright, was given to Charlie by his mother Megan Pace at Christmas when Charlie was eight years old (this can be calculated due to Liam's toy present, Voltron, popular in 1984 when Charlie would be eight). In a dream Charlie had of this scene, his mother said that with the piano Charlie would become successful and would "save" them. It remained with Charlie throughout his time in the band Drive Shaft, being used when Charlie composed new songs.
The piano was sold by Liam to pay for plane tickets for him, his wife, and his daughter to travel to Australia. It later appeared in another dream Charlie had where he played it, only to discover that Aaron was trapped inside it. The piano was then seen rolling out to sea.
The piano can be seen as a dramatic device to reflect Charlie's family. It was bought so that Charlie could become rich and thereby improve his family's standard of living. This is why the piano housed Aaron in a dream, as Charlie believed Aaron needed saving, and so this belief manifested itself inside an object that, to Charlie, symbolized the concept of saving.
Liam leaving a smoking cigarette on top of the piano with no regard may also symbolize Liam's attitude of not valuing Charlie in his idea of "family". This was reinforced by him selling the piano to help him, his wife, and child (what he saw as his family). Abandoning Charlie at the same time, the piano's departure demonstrated Charlie's loss of family.