You've had a long day, and you just want to play a game by yourself to relax. Your friends have other plans, however --- they see you're online, and they want to chat! Fortunately, Steam makes it possible to hide your status. Here's how to do it.
What Setting Your Status to Offline Does
Steam includes a variety of social functions, including chat and the ability to see what games your friends are playing. It's handy, and it makes joining up with your friends in multiplayer games a breeze.
If you don't want to participate, you can set your status to offline. Setting your status to offline completely disables all of the social functions Valve built into Steam --- you will not be able to send or receive messages, use voice chat, join (or be joined by) your friends in multiplayer games using Steam, broadcast, or view your friends' game-related stats.
Going invisible is an alternative to setting your status to offline. Setting your status to invisible will make you appear offline to all of your friends, but you'll still be able to send and receive messages, and use all of the other social functions Steam has to offer.
Setting your status to offline or invisible is different from setting Steam to offline mode. You can still play online multiplayer games with your status set to offline; you cannot when Steam is set to offline mode.
How to Go Offline on Steam
There are two places on Steam where you can change your status.
The first is the "Friends" menu, found in the top left. Click "Friends" and then click "Invisible" or "Offline," depending on your preference.
The other option is found in the "Friends & Chat" popup. Click on "Friends & Chat" in the bottom right-hand corner of Steam.
Click the small chevron (it looks like an arrow without the tail) to expand a drop-down menu, and click either "Invisible" or "Offline."
Just remember to set your status back to online --- or at least invisible --- when you're trying to use Steam's multiplayer's functionalities.