In official naming terms, 'minor' means something like 'modest' or 'humble', but here it does just mean 'junior'. Specifically 'the younger'. He wouldn't have been called Cicero Minor at the time as that would have been somewhat rude. He would have just been called Cicero like his father.
The way that we name people in modern terms is somewhat different to how they might have been named at the time. The 'Gaius Caesar' referred to in the excerpt in this article is the man we know as Julius Caesar. Gaius was his first name.
Likewise, Octavian is a name that we apply to the man before he became Augustus, but at the time, he was just called Caesar. We call him Octavian so we don't confuse him with his father.
"Minor" at that time must have corresponded to "Junior" now.
In official naming terms, 'minor' means something like 'modest' or 'humble', but here it does just mean 'junior'. Specifically 'the younger'. He wouldn't have been called Cicero Minor at the time as that would have been somewhat rude. He would have just been called Cicero like his father.
The way that we name people in modern terms is somewhat different to how they might have been named at the time. The 'Gaius Caesar' referred to in the excerpt in this article is the man we know as Julius Caesar. Gaius was his first name.
Likewise, Octavian is a name that we apply to the man before he became Augustus, but at the time, he was just called Caesar. We call him Octavian so we don't confuse him with his father.