What does the prime symbol indicate next to a lowercase or uppercase letter in music?

There are two main possibilities, depending on the context. When referring to pitches, it most likely indicates the octave a pitch is in, according to "Helmholtz notation":

An octave begins on the pitch C. Middle C is notated in this system with one prime, as c'; g' would be the G a fifth above it. An octave above middle C would take two primes as c'', and so forth.

In letters used for musical form, the prime symbol would likely stand for a varied repetition of a given section. For instance, while the written form ABA would indicate a literal, note-for-note return of the first A section (after the B section), the form ABA' would tell you that the A section is altered the second time around. Multiple primes can indicate further variants, as in ABA'BA''.