Take the key of C, for example. The notes of the C major scale are numbered:
C - I
D - II
E - III
F - IV
G - V
A - VI
B - VII
Now think of the triads you could build on each note. It will be
a major triad, a minor triad or a diminished triad:
C E G - major
D F A - minor
E G B - minor
F A C = major
G B D - major
A C E - minor
B D F - diminished.
When writing a number for a chord, we often use lower case for minor and upper case for major. So ii-V-I in C means the chords:
D F A
G B D
C E G
Finally, in jazz, seventh chords and higher extensions are part of the furniture. So reading between the lines, that could imply the chords:
D F A C
G B D F
C E G B |