It's the autosave icon; it indicates your game has been saved. There's a screen that explains that either when the game starts up or as one of the Loading Screen tips.

Disabling the startup movies

It is possible to disable the startup movies by editing the WillowEngine.ini file located in your Documents/My Games folder and commenting out a few lines which define which videos play when the game launches.

The default location for the Borderlands 2 config folder within your Documents folder is;

%USERPROFILE%\Documents\My Games\Borderlands 2\WillowGame\Config\

Simply edit the file 'WillowEngine.ini' and find the following variables:

[FullScreenMovie]
StartupMovies=2K_logo
StartupMovies=Gearbox_logo
StartupMovies=NVidia
StartupMovies=Loading
SkippableMovies=2K_logo
SkippableMovies=Gearbox_logo
SkippableMovies=Attract
SkippableMovies=NVidia

...and comment out the StartupMovies lines as follows;

[FullScreenMovie]
;StartupMovies=2K_logo
;StartupMovies=Gearbox_logo
;StartupMovies=NVidia
;StartupMovies=Loading
SkippableMovies=2K_logo
SkippableMovies=Gearbox_logo
SkippableMovies=Attract
SkippableMovies=NVidia

This should cause the game to skip over these startup movies when you start Borderlands 2.

Disabling the launcher

To disable the Borderlands 2 launcher, set the following launch option within Steam:

-NoLauncher

To change launch options with Steam, do the following;

• Right-click on 'Borderlands 2' under the game Library in Steam and select Properties
• Under the General tab click the 'Set launch options...' button
• Enter the launch options as per above and click OK
• Close the Borderlands 2's 'Properties' window and launch the game

This will disable the 'Play/Setup' screen upon launching Borderlands 2 from within Steam.

^{Sources: Disabling Intro Movies | Disable Launcher | How to set launch properties}