In answer to the OP (apologies for the essay-length reply):
Zoltan Kodaly (1882-1967) was a Hungarian with a traditional musical upbringing. His parents were amateur musicians and he remembered sitting under his mother's grand piano at the age of four, listening to her play Mozart, watching a beautiful sunset. He started composing in his teens and also taught at the Music Academy (later the Liszt Academy) in Budapest. There he was startled to find students who were fluent instrumentalists but who couldn't hear the music in their heads before they played it.
He, along with his contemporary Bela Bartok, travelled the Hungarian countryside collecting folk music.
At that time Hungary was a very oppressed country, heavily influenced by German culture, and had little sense of national identity (I believe that Hungarian was not the official language of the country until 1919).
These influences above made him think deeply about how to bring music, and musical literacy, to his country. He recognised the importance of an early start - 'nine months before the birth of the mother' was his reply to the question, 'When should music education begin?'
He felt passionately that early musical experiences should be of the highest quality (he expressed the opinion that if it had not been something of the calibre of Mozart that he heard his mother playing, he would not have become a musician).
Kodaly realised the intrinsic quality of folk music - he felt that, as it had been honed and polished over centuries, that it was a very pure form of music and that it contained many elements of art music, but in a smaller form. Thus, the experience and study of folk music would lead naturally to a study of art music. He also recognised that the voice was the best instrument through which to experience music first. Not only does everyone have one, but the inner hearing is activated when singing and musical concepts are experienced in quite a different way - singing is an internal skill - YOU make the sound - whereas playing an instrument is an external skill - you make something else make the sound. Anything learned through the singing voice has a different effect from learning it through an external instrument.
He visited the Cheltenham Three Choirs' Festival in the 1920s and was hugely struck by the use of relative solfa in the UK. This had been developed in the 19th century by Sarah Glover and then John Curwen. He realised that this was a powerful tool for the development of pitch awareness and skills, and that the related handsigns provided a kinaesthetic, visual tool for helping to train pitch acuity.
He and his colleagues and students travelled around Europe, collecting and learning about tools such as relative solfa and the rhythm names first developed in 19th century France.
Gradually they developed a collection of folk material and arranged it, and the acquisition of musical skills and knowledge, in a sequential order.
The first 'singing primary school' was set up in Kodaly's home town of Kecskemet in 1950. At one time there were over 200 of these schools - sadly, now, there are about 100. Kodaly wrote many pieces for children's choirs and the standard of choral singing rocketed.
It was in the early 1960s that people started to realise this quiet revolution in music education in Hungary and went to see for themselves. Yehudi Menuhin asked Kodaly to send someone to the UK to teach at his school and Cecilia Vajda (my first teacher) came in the late 1960s.
So - in a nutshell - this approach trains general musicianship using the voice. The approach is multi-sensory (and therefore very powerful and accessible by all types of learners). Kodaly recognised the three stages of learning - unconscious, making conscious and reinforcement. Folk music is used initially - of the indiginous culture to begin with - leading to a study of art music. With children we start with singing games - the folk music of the child - playground games.
Teacher training is considered to be of the utmost importance. Even kindergarten teachers in Hungary have a high level of musical training because it is recognised how important these early stages are. Kodaly said, 'A child will learn anything if there is someone who knows how to teach him.'
Musical literacy is a main aim - the ability to 'see what you hear and hear what you see'.
One of the beauties is that it doesn't matter what age you are, or what stage you are at in your musical development, there is something in the approach for you. Teaching in this way is the most exciting and rewarding thing I have ever done and it's why I'm passionate about it. Watching people develop their musical potential - helping people to do, or understand, something that previously eluded them - is the most satisfying experience.
Music meant very little to me until I stumbled across Kodaly and, over the years, I've lost count of the number of light-bulb moments that I've had. All the things I struggled with now made sense - it's an incredible feeling to succeed at something where previously you have failed.
I currently teach from age 3 to 70+. I have seen the benefits of this work with autistic children, those with learning difficulties including dyslexia and those with English as a second language; with 'privileged' children at a London conservatoire; with children in 'failing' primary schools, with very difficult home lives; and with adults who either want to learn to teach music better, or who want to improve their own musicianship. I teach professional classical musicians, keen amateur instrumentalists and singers, and a member of The Bootleg Beatles, as well as others with a non-classical background. Kodaly is taught at three of the major conservatoires, to undergraduates and post-graduates, in the UK.
It's difficult to express on paper the depth of the approach, but I've had a go.
Kodaly was a deep-thinking, philosophical man much ahead of his time in many ways. He felt strongly that 'music should belong to everyone' and that 'He who begins life with music will have this reflecting on his future like golden sunshine.' It is very easy to see this approach as just solfa, handsigns and rhythm names - but it is more than that - a whole philosophy of life and music.
As Kodaly said, 'Many people are looking for the door to the treasury of music in the wrong places. They keep hammering on the locked gates and pass right by the open door that is accessible to everyone.'