What are the benefits of drop bars?
The main advantage is more hand positions. With a regular flat bar, you hold your hands at the grips (with possibly about one more hand position available if you have bar ends).

With drop bars, you can hold at:


The brake hoods (on top of the brake levers)
The drops (the bottom part of the bar)
The tops (on the left and right of the stem)
That place between the hoods and the tops
Possibly others (or less of these, depending on who you ask).


For long rides, this makes a difference due to hand fatigue. 

A secondary advantage is you can also change how aerodynamic you are and your body geometry with respect to the bike by shifting around and using different hand positions relatively easily. For example, when you're in the drops, you're in a more aerodynamic shape versus sitting straight up with your hands on the tops. 



Drop bars aren't for everyone and do require proper setup (as do all bikes) and acknowledgement of the geometry of the bike. In particular, racers will likely set their bike up differently than tourers will (e.g. higher bars than racers), where its primarily a comfort thing. If you like doing long rides with flat bars and bar ends, more power to you. But for most people, the same bike won't work well with drop bars and flat bars because changing the bar changes the riding geometry.