It's the Steam Family Sharing program:
Steam Family Sharing allows family members and their guests to play one another's games (...) Once authorized, their library of Steam games becomes available for others on the machine to access, download and play.
This feature is currently (Dec 2013) in beta testing stage, available only for Steam users running the beta steam client (or so says Valve, I am running the Steam Client for Windows build Dec 3 2013, not a beta client), and who have joined the Steam Family Sharing Group (I did join the group).
How to share your game library:
First opt into the latest Steam Client Beta Update. Then, Family Sharing is enabled in one of two ways: You can either locally authorize a device to share via the Account tab in Settings, or respond via email to a user’s Steam request to share your previously installed games
Sharing doesn't work on a per-game basis, but your whole library (except some games such as "titles that require an additional third-party key, account, or subscription")
You can only share to 10 devices at a time, and a shared library may only be accessed by one user at a time. "If you decide to start playing when another user is already playing one of your games, he/she will be given a few minutes to either purchase the game or quit playing."
Borrowers will have access to DLC and in-game items, and are able to "purchase, trade, earn, or otherwise acquire in-game content", but these items go the the original owner's account.
Region restrictions "remain in place when lending or borrowing content."
If the borrowers commit abuse, cheat, fraud, etc, "your Family Sharing privileges may be revoked and your account may also be VAC banned"
(excerpts in quotes taken from the official page)