What is the "sandbox"?

"The Sandbox" of Bungie

In the particular case of Bungie, "The Sandbox" refers to all the things with what a player can directly interact, for instance in Destiny. That is also what Jon Weisnewski, working at Bungie, is saying in his resume :

The Sandbox team is responsible for controller input, the "feel" of moving through the world and performing actions, player abilities, grenades, melee, vehicles, weapons, armor, and custom sandbox content to support activities like Raid Relics, Scorch Cannon, etc.

The Sandbox term in gaming

The Sandbox term usually corresponds in gaming to an area in which the user is free to do what he wants.

If refers to the notion of sandbox game :

A game wherein the player has been freed from the traditional structure and direction typically found in video games, and is instead given the ability to choose what, when, and how they want to approach the available choices in content. The term is in reference to a child's sandbox in which no rules are present and play is derived from open-ended choice. While some sandbox games may have building and creation aspects to their gameplay, those activities are not required. Sandbox games usually take place in an open-world setting as to facilitate the freedom of choice a player is given.

It is called sandbox because you are able to do whatever you want there, like in a real sandbox: you are the one building your adventure. You are in a world where you can walk around and go for your own objectives. There is a lot of existing exemples of sandbox games, such as Minecraft, The Elder Scrolls games, Kerbal Space Program, Garry's Mod, Don't Starve, or EVE Online.

A sandbox is a style of game in which minimal character limitations are placed on the gamer, allowing the gamer to roam and change a virtual world at will. In contrast to a progression-style game, a sandbox game emphasizes roaming and allows a gamer to select tasks. Instead of featuring segmented areas or numbered levels, a sandbox game usually occurs in a “world” to which the gamer has full access from start to finish.

A sandbox game is also known as an open-world or free-roaming game.

Ref

Basically in a sandbox game you don't have a linear mission path you need to follow (or if you do, you also have the sandbox option to explore), but instead you can do whatever you want, and whatever the game limits maybe. Prime examples are GTA and Minecraft.

"The Sandbox" refers to the things a player can do as part of gameplay; i.e. the weapons, vehicles, and abilities available to the player. This can also refer to the enemies or environmental hazards the player deals with as well.

As far as I know this is a particular quirk of Bungie's (and 343 Industries' in continuing Bungie's legacy) so I'll furnish some proof of this usage:

LinkedIn profile of Jon Weisnewski - https://www.linkedin.com/in/jon-weisnewski-455b6b13

Interview with Ken Kato - http://speakhertz.com/6706/interview-343-industries-audio-manager-ken-kato