What does a Roman numeral 1 with a superscript 6 mean?

Question

The image above is a functional chord symbol. But what does the number mean?

Answer 1

This means a minor "one" chord (minor triad built on the tonic) in first inversion. The 6 is short for 6-3 (both superscripted, with the 6 above the 3), meaning that the chord is arranged (voiced) with a sixth and a third above the lowest pitch. The sixth and third can be displaced by one or more octaves. For example i6 could mean a sixth and a tenth above the lowest pitch.

Answer 2

Lower-case 'i' means the tonic chord of a minor key. The superscript '6' means first inversion. Intervals of a 6th and a third above the lowest note (the '3' is assumed.)

Note that 'Cm6' (with an explicit letter-name) means something different. That's 'C minor sixth', a C minor triad with an added A.