What does 'a character-driven story' mean?
A character-driven story is one that focuses on the personal motivations and desires of the protagonist and secondary characters. As such, the characters create the plot, or have significant influence on what happens. Character-driven stories are normally associated with soul-searching or introspective dramas, and usually lauded above plot-driven stories, but this need not be the case. For example, Die Hard is a character-driven thriller with a great plot led by John McClane, which is why it's a classic. Raiders of the Lost Ark is a plot-driven adventure, with very high stakes and an engaging hero (who fails at every attempt he makes within the plot), which is why it's a classic.
Most great TV dramas are character-driven, like The Wire, Mad Men, Cracker etc, while some great TV like Dr Who are plot-driven. 'Character-driven' doesn't mean 'there is no plot', just as good plot-driven stories doesn't necessarily mean 'there are no decent characters', although that can happen frequently.
Character Vs Plot
Sub-plots & Secondary Characters