The pistol in your photo is a pre-World War 1 German-made "Reform" pocket pistol, caliber .25 ACP.  These kids of pistols were very popular between 1905 to 1914.  The "Reform" Brevete Pocket Pistol is sometimes called a "rising bar" -- from its four (4) shot barrel cluster -- repeating pistol.  The pistol barrels are loaded with four .25 ACP cartridges and the cluser is loaded into the pistol frame like a conventional automatic pistol's magazine.  The lever on the side is a manual safety. 

 

When the gun is ready to fire, the safety is set to OFF and the trigger is either cocked or pulled (the pistol is both single action and double action).  The hammer falls firing the cartridge.  When the hammer is cocked again, the barrel cluster moves up one barrel to align the next cartridge in the stack with the firing pin.  When the hammer falls on the second cartridge, part of the buring propellant gas is vented to the upper barrel to eject the spent first round.  Rounds three and four are fired in a similar manner except the fourth round is not ejected.  The barrel cluster is then removed and a loaded cluster replaces the first.  The fourth fired cartridge has to be manually removed from the original barrel cluster.  This pistol was designed by August Schuler.  Excellent condition pistols of this kind can sell for $1800 to $2500 to collectors of such curios and relics.

Typo: change ". . . kids . . . " to " . . . kinds . . ."

 

This type of pistol is considered a "repeater" because it will fire four shots.  It is very similar in concept to the Sharps four-shot Derringers of the 19th centry.  These were single action pistols that had a rotating firing pin. For each cock of the hammer the firing pin rotated 90 degrees to fire one of the four paired barrels.

 

A more modern variation is the double action only (DAO) COP 357 derringer in .357 Magnum.  Now a defunct company, COP, Inc. of Torrance, CA was the manufacturer of the COP or Compact Off-duty Police pistol.  The derringer was very well made of stainless steel, compact [5.6"x1.1"x4.1"], and light [1.75 lbs.].  But, it was more expensive than similar pocket pistols of its size (though they weren't as powerful) and its specialized nature led to discontinued manufacture.  Used pistols are still quite popular.