The Savage 1907 is the first in a line of semiautomatic pistols produced by the Savage Arms Company (named for its founder, Arthur William Savage) beginning in 1907. It is sometimes erroneously referred to as the 'Savage 1905' because the only year marked on the early guns is that year, indicating when the patents used in its design were awarded.
The 1907 is chambered in .32 ACP (also referred to as .32 Automatic or 7.65 Browning, the latter in Europe generally). This was an extremely popular civilian handgun cartridge in the early 20th century, and many so-called 'pocket pistols' were chambered for it. Although it would be mostly supplanted in duty and service pistols during World War One - which saw the widespread adoption of both the .45 ACP and the 9mm Parabellum as well as several other 9mm variants such as 9mm Kurz(.380), the Spanish 9mm Largo and the Italian 9mm Glisenti.
It holds a double stack box magazine capable of holding ten rounds of .32 ACP; for a semiauto of its time, that was an impressive capacity. The gun was advertised heavily for self defense, with advertisements showing women using it to fend off multiple attackers. The most common slogan was 'Ten Shots Quick!' Savage capitalized on this by getting testimonials from contemporary celebrities, such as William Cody and William Pinkerton, running alongside text asserting that the Savage would "fight like a fiend" to defend your wife should she need to use it.
The 1907 is a delayed blowback firearm. As such, it has a moving removable barrel instead of a fixed barrel mounted to the frame of the gun.
it is nominally a delayed blowback - the barrel has a cam which fits into a channel in the top of the slide. The channel bends near the rearmost position; the theory is that when the gun fires, the slide and barrel are locked together by a single lug at the bottom of the barrel. As the slide moved backwards under the recoil impulse, the barrel would rotate due to that cam, unlocking the slide and permitting it to move backwards, extracting, ejecting and chambering a new cartridge. This, it was claimed, would delay the opening of the chamber long enough for the pressure to drop far enough to make this a safe operation. There are conflicting stories as to whether this mechanism actually works as intended, but everyone seems to agree that the 1907 is a quite reliable pistol even if it's just a fancy blowback design.
Several iterations of the gun would be produced between 1907 and 1929 when it was discontinued - the 1907 had many of its features modified and tweaked. The next major model was the model of 1915 in an attempt to regain market share being lost to bigger and more modern pistols. This included a version in .380/9mm Kurz to try to address the increasing popularity of larger cartridges. In 1920, the model of 1917 (yeah, the name is silly) was released, the last major revision of the gun.
Over a quarter of a million of this series of gun was produced (1907/1915/1917 in .32 and .380). In addition, there was a very small number (less than 300) produced in .45 ACP, known as the 'Government' model. Those pistols were produced for the pistol trials in which they competed against John Moses Browning's famous design which would become the 1911.
Sources:
Savage Arms: An Overview of the History,Development and Classification of the .32 and .380 Semi-automatic Pistols (Waldemar Goulet, Ph. D.)
Savage Automatic Pistols: Overview (Ian McCollum, Forgotten Weapons)
http://www.thetruthaboutguns.com/2013/10/jeremy-s/obscure-object-desire-savage-1907-45-pistol/ (The Truth About Guns, by 'Jeremy S')
Personal experience with the 1907