The current champion of digital storefronts on PC is Steam, first released by Valve in 2004 as a way to distribute their own games. It currently lacks successful direct competition, but there are other successful storefronts, such as gog.com, which offers strictly DRM-free games and specialises in preserving older PC games, and Origin, a storefront exclusively for games made by Electronic Arts. Currently, physical distribution of computer games is practically extinct due to the convenience of the digital storefront.
While consoles have had digital storefronts since the early 2000s, such as the WiiShop, physical media remains popular. This may be a result of early digital storefronts on console being more of a gimmick, used for small games and demos rather than full game releases, or the "plug-and-play" model that console games had in contrast to computer games for a long time. However, the "plug-and-play" model doesn't apply very well to modern video game consoles, as games usually require being installed from the disk to internal storage to be able to run properly, and receive updates.
Digital games don't take up physical space
You can purchase, installed and play a digital game without leaving your home or waiting for a delivery
Digital games have negligible distribution cost, allowing small developers to release games
A digital game can be downloaded again if lost or destroyed
The game must be downloaded before it can be played
Downloaded games take up limited storage space
You may lose access to the game if the company denies you service or the servers go down
Digital games cannot be sold second-hand