The Moro tribesmen in the Philippines had a pre-battle ritual involving the chewing of coca leaves and tying wet rawhide thongs around their testicles. The rawhide would dry and shrink, putting constant painful pressure on their testicles. Once they had become used to the pain (or dulled sufficiently from the coca) they would attack, believing that if they could withstand that kind of pain, not much else would stop them. (No, I am NOT making this up)
The prevalent round at the time was the .38 S&W, and proved to be an insufficient manstopper against the coked-up, ball-squeezing Moros who would take round after round from the .38 and keep on attacking, usually living well long enough to inflict serious if not lethal injuries against their American 'subduers' before they bled out. It was decided at that time that something that would not only prove lethal but had sufficient stopping power to make even a drug-hazed Moro pause and reflect was required.
A few of the troopers in the Philippine Campaign had .45 Colt SAA 'Peacemakers' left over from the 'good ol days' and anecdotal evidence sent back to the War Department indicated that with decent bullet placement, a .45 would generally do the trick, but the .45 Peacemaker was by now considered somewhat fragile and obsolete in the face of much newer technology (i.e. the self-loading pistol).
The basic concept of the modern day 1911 had already been designed by John Browning and introduced by Colt by the turn of the century. It was agreed that the .45 ACP cartridge (basically a scaled-up .38 Colt Auto or 'Rimless') was suitable (after testing vs. the 9mm, which was then prevalent in Europe), but the handguns then available for the cartridge did not suit themselves well to a combat environment due to poor handling and field (i.e. cleaning/maintenance) characteristics. As already noted, Browning's 1905 redesign in .45 ACP (an updated, somewhat beefier version of his M1900, originally chambered itself in .38 'Rimless') was pitted against the 1908 toggle-action design submitted by George Luger. The Browning pistol was conditionally accepted and adopted as the M1905 due to ease of mass assembly, reliability, and cost to produce. The Luger design (an improvement over the original Borchardt toggle design) had many expensive machined parts that required careful fitting and close tolerances, and was by comparison, insanely expensive to mass-produce.
The M1905 was produced from 1905 to 1911, being replaced by the M1911 in late 1911. Additional modifications were added in 1913 to the safety system, and this weapon was produced until signficant modifications were adopted in 1924, resulting in the M1911A1. The 1924 design has remained fundamentally unchanged since.