How can Emma be considered a novel of education?

The education of Emma Woodhouse constitutes an important—perhaps the most important—element in the story. The prominence of the theme can be seen at the start of the book, where we're given a detailed description of Emma's educational background.
Education in relation to Emma, however, is not just academic; it relates to her induction into polite society, with its bewildering array of conventions that govern relations between men and women. As a woman in Regency England, Emma is not expected to be academically gifted; she is, however, expected to be able to know how to conduct herself in society.
That's where Miss Taylor comes in. Or is supposed to, at any rate, because Emma's governess is more of a dear friend than a disciplinarian. Due to the closeness of their friendship, Emma is somewhat lacking in the necessary moral guidance by the time she comes of age. This gives her an overweening self-confidence that manifests itself in her constant interference in other people's lives. Emma is so full of herself, so certain that she's always right, that she overlooks the potential harm that her experiments in matchmaking can so easily cause.
To some extent, this isn't Emma's fault. The problem is that she's never really had much in the way of moral education in her life. As we've seen, Miss Taylor was always more of a pal than a governess. It takes the stern, though well-meaning, admonitions of Mr. Knightley to show her the right way forward. But Knightley can only suggest; he cannot turn Emma into a properly mature young lady, no matter how hard he tries. This is something she must learn to do for herself.