In WWI the army was needed more semi-auto pistols than were available or that could be produced in time. The moon clip was developed so that the rimless .45 ammo could be used in S&W Revolvers. Without rims, the revolvers would not otherwise be able to extract the cases.
Using .45 revolvers helped alleviate the handgun shortage and allowed a single caliber of ammo to be used by all U.S. troops whether they had a revolver or sem-auto pistol.
Originally, half-moon clips were used. These held only two or three rounds. Modern full moon-clips hold 6, 7 or 8 rounds, and allow a full cylinder to be loaded/unloaded at once.
The increase in speed and ease of loading/unloading was mostly a side benefit, the intent was primarily to be able to use rimless cases in a revolver.