In addition to his more substantial pieces that others have mentioned, the real turning point in his music was a very small piece called Für Alina:

https://www.youtube.com/watch?v=jvXy69eF__Y

Prior to this he had composed in the dissonant, serialist style that was expected of "serious" art music in the middle of the 20th century. This was the first piece where he broke with the contemporary style and introduced his unique "tintinnabuli" style.

If you have even a basic familiarity with music theory it's worth taking a look at the structure of the piece because it's surprisingly simple for the effect. As the right hand plays the melody, the left hand simply plays notes from a b minor chord, with the particular note being whatever is just beyond one octave below the note that the right hand is playing. However there is one exception towards the end where the left hand plays a C# instead of a D as it would be expected to, and this marks the climax of the piece.