The idea:
Being able to tag certain games in your library, similar to how you can favorite games or put them into a category. The tag itself should be something along the lines of "Looking for friends to play with" or "willing to play".

Then once you have tagged the game like this, your friends will be able to see your tag on the game similar to the "these friends own this game" and "these friends previously played this game" feature.

The reasoning behind this feature is to get people to play more games with their friends. Including steam friends who they don't really talk to anymore. Out of respect for your privacy and generally not wanting to bother you, most (older) steam friends likely won't actively message or invite you into games unless you talk to them regularly.

This feature will essentially quietly "announce" that you're open to play a certain game with your friends. It's like a passive invitation for others to play with you. You'll be able to mark lots of games using this feature that you otherwise would not really play anymore. Especially social games that otherwise take a lot of organizing. So instead of having to invite friends to ask them whether they're even interested in the first place, they will automatically know that you're up to playing it.

This could also help when browsing for new games. I imagine it will be a lot easier to purchase a new game from the store when you notice dozens of friends who are willing to play.