In Pygmalion, in Act I, Higgins predicts that, given six months, he'll be able to take Liza "anywhere and pass her off as anyone." He also makes it clear that her accomplishment will be based on her "ear" and "tongue." In fact, he modifies his prediction to say that "if she has a good ear and a quick tongue," his task will take only three months.
The expressions "good ear" and "quick tongue" are representative of the trope metonymy, which is a literary device comprising figures of speech. Metonymy replaces a general concept or an idea with a word representing a concrete object. Therefore a good "ear" refers to the ability to accurately hear various sounds and the fine points that differentiate sounds, while a quick "tongue" refers to an adroit facility in reproducing variations of similar verbal sounds. In other words, possessing a "good ear" and a "quick tongue" means that the individual can recognize and articulate the different pronunciations of a newly introduced language sound system.
In Act III, Higgins tells his mother that Liza gets on "like a house on fire" (really quickly) and attributes this to his earlier predictions being correct: "she has a quick ear." He claims that he will fulfill his prediction (the six month prediction, not the overly enthusiastic three month prediction) and in "six months time" introduce her anywhere and "pass her off as a duchess," thus making him confident that he will win his bet. In summary, Higgins says Liza is an apt pupil because she recognizes audible differences in phonetic sounds and is able to articulate the differences accurately.