The I-iii-I6 progression is a chord sequence that moves from the tonic chord (I) to the mediant chord (iii) and returns to a first inversion tonic chord (I6). This progression showcases the relationship between the tonic and mediant chords, creating smooth voice leading while adding a subtle color to the harmonic texture. The use of the I6 inversion helps to connect the chords more effectively and can serve to enhance the emotional quality of a piece.