the ability and tendency to determine what should be done and to start doing it without instruction
to start something
The exact meaning of starting something depends upon the context. For example:
"She did it on her own initiative." — started it without anyone telling her to
"She seized the initiative." — started actions that force others to react to her rather than her having to react to them
"the peace initiative" — a plan or the start of actions to bring about something
"a ballot initiative" — a proposed law that is started by citizen petition rather than by the legislature (applicable in many jurisdictions such as California)
The four or five remaining hours before nine o'clock arrived, Andrea employed in riding, paying visits,—designed to induce those of whom he had spoken to appear at the banker's in their gayest equipages,—dazzling them by promises of shares in schemes which have since turned every brain, and in which Danglars was just taking the initiative.
Chapters 95-96 (72% in)
There are no more uses of "initiative" in The Count of Monte Cristo.