Gatsby's characterization of Daisy's voice can probably best be read as an accurate metaphor or as a way to symbolize the meaning of Daisy's character. She is objectified here as a symbol of wealth for Gatsby but she is also a fully developed representative of the habits and mores of the wealthy elite when seen in the larger context of the novel.
The metaphor describes a truth about Daisy's character both for Gatsby as a striving, ambitious and romantic figure and for the narrative as a whole wherein Daisy is used to represent certain qualities and perspectives.
Notably, when Gatsby proclaims that Daisy's voice is full of money, Nick seems to think that Gatsby has found the perfect description.
“Her voice is full of money,” [Gatsby] said suddenly.
That was it.… That was the inexhaustible charm that rose and fell in it, the jingle of it, the cymbal’s song of it.…
If Nick agrees (as the narrator of the tale) and corroborates Gatsby's assessment of Daisy's most prominent and alluring trait, we can take the idea that her voice is full of money as a truth about Daisy.
In a novel where appearances prove often to be false, we have to look hard to find moments where the truth burns through the facade. For Daisy, this happens when she encounters the beautiful shirts in Gatsby's house and sobs over them. She is depicted as a person who seeks to gratify her desires, eschewing marital and/or parental obligations, willing to play at an affair with a wealthy man from her past, but unwilling to take responsibility for the consequences of her actions.
Daisy is, in short, a person of great entitlement. We see the ways that money can insulate people from personal obligations and even from legal responsibility but we see more principally the idea that money allows adults to lead a life of play. This idea is connected to notions of glamour and pretense. Ultimately the notion that wealth corrupts comes to be associated very closely with the idea that these rich figures are not compelled to honestly be themselves and instead take on roles that suit them in the moment.
Given this point of view as to the significance of wealth in The Great Gatsby, Gatsby's claim that Daisy's is thoroughly connected with money even down to her speaking voice serves to situation Daisy within the narrative. She plays a role with Gatsby then plays a different one after running down Myrtle in the street. Daisy is free -- or feels free -- to continue to play a part, to be dishonest, to be removed from responsibility because she is wealthy.
Daisy exhibits all of the un-reflective moral corruption of her ilk.
Of perhaps equal importance is the idea that Gatsby seeks to attain Daisy. She is, for him, a symbol of wealth. Thus, Daisy's symbolism is doubled in the sense that she represents the moral shallowness of the wealthy elite and stands as the defining object of wealth for Gatsby.
If the novel suggests that the rich elite are capable of treating other people as objects and ignore the subjective humanity of others, it is fitting that they are also given an objectified symbol in Daisy.