What is the difference between financial and operating leverage? Why
are these concepts important to an organization?

Financial leverage relies on debt instruments to boost the firm's
return on equity.  In contrast, operating leverage is based upon the
company's cost structure rather than its capital structure. 
Specifically, it is the mix of variable and fixed costs that comprise
the firm's cost structure.  Both affect a firm's potential risk and
reward.

A good description with examples can be found at "Operating Leverage"
Huntington http://partners.financenter.com/huntington/learn/guides/smbizfinancing/sboperat_leverage.fcs

Sincerely,

Wonko